Do you have any suggestions for helping my 13 year old deal with his grandmother's dementia?

Make sure your son understands what Alzheimer’s disease is. Kids often fear they can catch it like you can catch a cold. One way to help him understand memory loss: Tell him that his grandmother's brain is experiencing what happens when he forgets to click on "save" when he's working on a document on his computer; she can't remember recent events because her brain didn't "save" them.

You might begin to talk to him about the things he can still do with him grandmother. Start with one activity they both enjoy. Build on successes. Some Alzheimer’s chapters have support groups for young people; call yours to see what resources are available. The Alzheimer’s Association’s web site has a section for teenagers that he can research. 

Another possibility: I wonder if he's jealous. Are you getting someone to stay with Grandma while you do things just with your son? That's important. Teenagers have a tough time with growing into an adult and this is an added stressor for them. Be patient with him and he may end up being a great help with his grandmother.