Step One (Signatera Assay Development) Inclusion Criteria:  Surgically resected and histologically/pathologically confirmed stage II cutaneous melanoma. No more than 16 weeks may elapse between final surgical resection and randomization. Treatment should start only after complete wound healing from the surgery. Participants must not have been previously treated for melanoma beyond complete surgical resection. At least 18 years of age. Ability to understand and willingness to sign an IRB approved written informed consent document (or that of legally authorized representative, if applicable).  Step One (Signatera Assay Development) Exclusion Criteria:  A history of other malignancy with the exception of malignancies for which all treatment was completed at least 2 years before registration and the patient has no evidence of disease or malignancies in situ (such as DCIS), basal cell carcinoma, or localized cutaneous squamous cell carcinomas. Currently receiving any other investigational agents. Prior history of pneumonitis A history of allergic reactions attributed to compounds of similar chemical or biologic composition to atezolizumab and tiragolumab or other agents used in the study. Significant cardiovascular disease (such as New York Heart Association Class II or greater cardiac disease, myocardial infarction, or cerebrovascular accident) within 3 months prior to initiation of study treatment, unstable arrhythmia, or unstable angina.  Active or history of autoimmune disease or immune deficiency, including, but not limited to, myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, antiphospholipid antibody syndrome, Wegener granulomatosis, Sjögren syndrome, Guillain-Barré syndrome, or multiple sclerosis, with the exceptions listed below:  Patients with a history of autoimmune-related hypothyroidism who are on thyroid replacement hormone are eligible for the study. Patients with controlled Type 1 diabetes mellitus who are on an insulin regimen are eligible for the study. Patients with eczema, psoriasis, lichen simplex chronicus, or vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis are excluded) are eligible for the study provided all of following conditions are met:  Rash must cover < 10% of body surface area  Disease is well controlled at baseline and requires only low-potency topical corticosteroids No occurrence of acute exacerbations of the underlying condition requiring psoralen plus ultraviolet A radiation, methotrexate, retinoids, biologic agents, oral calcineurin inhibitors, or high potency or oral corticosteroids within the previous 12 months Active tuberculosis. Prior allogeneic stem cell or solid organ transplantation Positive hepatitis B surface antigen (HBsAb) at screening. Positive hepatitis C virus (HCV) antibody test at screening (unless followed by a negative HCV RNA test). Current treatment with anti-viral therapy for HBV Positive Epstein-Barr virus (EBV) viral capsid antigen immunoglobulin M (IgM) test at screening. An EBV PCR test should be performed as clinically indicated to screen for acute infection or suspected chronic active infection. Patients with a positive EBV PCR test are excluded. Prior treatment with CD137 agonists or immune checkpoint blockade therapies, including anti-CTLA-4, anti-PD-1, anti-TIGIT, and anti-PD-L1 therapeutic antibodies. History of severe allergic anaphylactic reactions to chimeric or humanized antibodies or fusion proteins Patients with HIV are eligible unless their CD4+ T-cell counts are < 350 cells/mcL or they have a history of AIDS-defining opportunistic infection within the 12 months prior to registration. Concurrent treatment with effective ART according to DHHS treatment guidelines is recommended.  Step Two (Randomization and Treatment) Inclusion Criteria:  Positive ctDNA test.  Normal bone marrow and organ function as defined below:  Absolute neutrophil count ≥ 1,500/mcL Lymphocyte count ≥ 500/mcL Platelets ≥ 100,000/mcL Hemoglobin ≥ 9.0 g/dL (patients may be transfused to meet this criterion) Total bilirubin ≤ 1.5 x IULN or direct bilirubin ≤ IULN for participants with total bilirubin levels > 1.5 x IULN; patients with known Gilbert disease must have total bilirubin ≤ 3 x IULN AST(SGOT)/ALT(SGPT) ≤ 2.5 x IULN Alkaline phosphatase ≤ 2.5 x IULN Creatinine clearance ≥ 45 mL/min by Cockcroft-Gault Serum albumin ≥ 2.5 g/dL INR or PT ≤ 1.5 x IULN unless participant is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of intended use of anticoagulants aPTT ≤ 1.5 x IULN unless participant is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of intended use of anticoagulants ECOG performance status ≤ 1 The effects of atezolizumab and tiragolumab on the developing human fetus are unknown. For this reason, women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control, abstinence) prior to study entry and for the duration of study participation, for 90 days after the final dose of tiragolumab, and for 5 months after the final dose of atezolizumab. Should a woman become pregnant or suspect she is pregnant while participating in this study, she must inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of the study, and 90 days after completion of the study  Step Two (Randomization and Treatment) Exclusion Criteria:  Pregnant and/or breastfeeding. Women of childbearing potential must have a negative pregnancy test within 14 days of study entry. Treatment with a live, attenuated vaccine within 4 weeks prior to initiation of study treatment, or anticipation of need for such a vaccine during study treatment, within 90 days after the final dose of tiragolumab, or within 5 months after the final dose of atezolizumab Treatment with systemic immunostimulatory agents (including, but not limited to, interferon and IL-2) within 4 weeks or 5 drug-elimination half-lives (whichever is longer) prior to initiation of study treatment.  Treatment with systemic immunosuppressive medication (including, but not limited to, corticosteroids, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor-α [TNF-α] agents) within 2 weeks prior to initiation of study treatment, or anticipation of need for systemic immunosuppressive medication during study treatment, with the following exceptions:  Patients who received acute, low-dose systemic immunosuppressant medication or a one-time pulse dose of systemic immunosuppressant medication (e.g., 48 hours of corticosteroids for a contrast allergy) are eligible for the study Patients who received mineralocorticoids (e.g., fludrocortisone), corticosteroids for chronic obstructive pulmonary disease (COPD) or asthma, or low-dose corticosteroids for orthostatic hypotension or adrenal insufficiency are eligible for the study. Major surgical procedure within 4 weeks prior to initiation of study treatment, or anticipation of need for a major surgical procedure during the study. Severe infection within 4 weeks prior to initiation of study treatment, including, but not limited to, hospitalization for complications of infection, bacteremia, or severe pneumonia, or any active infection that, in the opinion of the investigator, could impact patient safety Treatment with therapeutic oral or IV antibiotics within 2 weeks prior to initiation of study treatment. Patients receiving prophylactic antibiotics (e.g., to prevent a urinary tract infection or chronic obstructive pulmonary disease exacerbation) are eligible for the study. Treatment with systemic immunostimulatory agents (including, but not limited to, interferon and IL-2) within 4 weeks or 5 drug-elimination half-lives (whichever is longer) prior to initiation of study treatment.