As a generalization, carcinogens cause additional cell multiplication, which increases the chances of mutations. Multiple mutations under any circumstance is probably carcinogenic. An example of a non-mutagenic, yet carcinogenic compound is asbestos. There are examples, at first examination, of chemicals that are mutagens, but seem not to induce cancer. These, however, tend to be classed as both mutagenic and carcinogenic after more detailed study.
Cancer is one phenotype of mutagenicity.
This is why we test for mutagenesis and attempt to avoid the culprits.