There were already 7 known variations when the vaccines were introduced. Furthermore, none of the vaccines currently approved for use (at least in the US) have

There were already 7 known variations when the vaccines were introduced. Furthermore, none of the vaccines currently approved for use (at least in the US) have the live virus. So vaccines are not "causing mutations". Mutations happen during replication within infected cells. The vaccines will greatly reduce the number of cells that will get infected. So vaccines reduce mutations and chances of strains to take hold. Unvaccinated people who become infected are what will fuel strains.