Of course, we can never stop all mutations. However, for mutations to be useful for the virus, they do need to happen at an evolutionary scale. Especially because we're lucky that SARS-CoV-2 mutates much slower than Influenza and HIV.
If the rate of transmission reaches the elusive herd immunity, the time-frame for the virus to evolve into evading vaccines grows significantly longer, even with a non-zero mutation rate.
Lastly, antibodies created via the mRNA vaccines have a broader binding affinity to different variants than those from natural immunity [1].
Again, the goal is to not eradicate, but to scale it down to the point where it is statistically not a threat.