The essential tools for tree cutting and removal include a chainsaw, which is crucial for cutting through large branches and trunks, and a hand saw for smaller branches and precise cuts. An axe or hatchet is useful for chopping smaller branches and making notches, while a pole saw helps in reaching high branches without a ladder. Rope and rigging equipment are necessary for safely lowering large branches and sections of the tree. Additionally, personal protective equipment (PPE) such as gloves, safety goggles, a helmet, and hearing protection are vital for ensuring safety during the process.