During which phase of the cell cycle do mutations occur?

if it is a gene mutation then it is during the S phase, and if it is a chromosome mutation, then during metaphase or anaphase.

Gene mutation has to do with the duplication of the DNA, and if something wrong goes with this duplication, then the new DNA will not be exactly like the original one. This duplication happens in the S phase. Chromosomal mutation are either having an extra or missing piece, or having an extra or missing chromosome. An extra or missing piece happens during crossing over where the exchanged parts both go to one side, so one side has an extra chromosome piece and the other has a missing one. This happens in metaphase. Chromosomal mutation could also be an extra or missing chromosome and this happens due to nondisjunction in the anaphase.