How does the MMR vaccine work?

Answer 1

The MMR Vaccine contains tiny doses of living but inactivated viruses that cause measles, mumps and rubella. Once these viruses are injected into the body, the immune system will develop certain antibodies against these three diseases shortly following vaccination. Because your body has memory cells it now knows how to defeat these diseases when they enter the body again, and it will know which certain antibodies it needs to produce; these antibodies in your body will give a lifelong protection against these diseases.

Answer 2

There are a couple different types of vaccinations, but most contain partially-dead viruses. This allows the immune system to build up against the virus, but it's not active enough to cause infection.

Also, mumps is a viral infection, and thus are unaffected by antibiotics (which kill bacteria, not viruses). Viruses are pretty much incurable, except by giving your immune system time to kill it.