Blood work showed I am only not immune to mumps only but I got the MMR vaccine two years ago. Is this possible? Safe to get it again?

It is safe. For some reason your body did not make any antibodies in response to the first MMR. I would definitely get a second dose and then blood work to see if it "took".
Yes/safe. Sometimes you can actually be relatively safe after such a vaccine but the blood test may not show an antibody level high enough to reach what is considered a protective level. It is okay to get these vaccines repeatedly.Only if you had a bad reaction to some of the components of a vaccine in the past would it be avoided in the future.