The virus will mutate no matter what regardless of vaccine. It's not the vaccines that are driving mutations. The vaccine basically programs a set of immune system regex stream filters. Maybe some mutants get past it, well then the immune system will generates another response to it as it goes on to infect other cells in the body etc...

Some of the original variants are thought to have arisen out of immuno-compromised pre-vaccinated patients. Maybe they got IVIg, monoclonal antibodies, or convalescent plasma.