But don't forget that the vaccine also forces the virus to mutate in order to defeat it.
Not more then your own healthy & effective immune system does it anyway.
Vaccines actually reduce the virus mutation risks since due to vaccination immune response is a) faster, b) stronger and c) therefore more efficient. But when you get infected by a virus for the first time your own immune system has to figure out on its own, impromptu, how to deal with the virus & the infection. In some people such fight is very efficient in some is not - and in those people virus has a chance to mutate & escape. Mind: the longer the fight in your body goes on, the more chances virus has to adopt, to mutate & to escape & spread around!
What a vaccine does is it prepares & train your immune system to quickly & efficiently respond to a virus invasion. To think vaccines boost virus' chance to mutate is moronic. Virus mutations are much more present in hosts who are dealing with the patogen the first time. While due to vaccination your immune system identifies the pathogen (it's S-protein) instantly, thus reducing chances for mutation.
But mind SARS-CoV-2 already has some incredible mechanisms when it comes to the immune system evasion - within its in-cell replication mechanism. Very similar mechanism eg. HIV & herpes viruses have. Eg. ability to hide its mRNAs inside the mitochondria wall (creating protective bubbles) so the in-cell immune mechanisms can't be triggered. Or eg. creating multicore cell structures (syncytia) by merging the infected cells for much more effective virus replication. There are also some indications SAC2 is able to merge infected cells with lymphocytes (and create such syncytia) to avoid immune response completely - that's a mechanism cancer cells / tumors are capable of. And that's f... scary! SARS-CoV-2 is a very, very nasty virus.
That's not how mutations work.
Mutations is by chance.
True. The better chances & environment for replication the virus has, the greater is a chance for mutation to be created, to be such to evade the immune system & to escape to host's body & spread around. So, the quicker your immune system deals with teh virus & destroys it, the lower chances the virus has for its replication within your cells and thus for mutations. And vaccines help to train your immune system to be more prepared to deal with the virus when it invades your body. Vaccines are good for you, not bad.