The catalytic mechanism of topoisomerase involves transiently breaking one or both strands of the DNA helix to relieve torsional stress. It can be divided into two main types: Topoisomerase I and Topoisomerase II. While Topoisomerase I makes a single-strand break, Topoisomerase II creates a double-strand break. Both types utilize a catalytic tyrosine residue to form a covalent intermediate with the DNA, facilitating strand passage or relaxation.