Do a google of "convert mesh to obj". a couple links seemed to look promising.
The issue is I do not know if ".mesh" format is a standard or is application specific. I have never seen .mesh as an output type for any applications I have used. I did see some mentions of blender and lightwave.
But the idea is you want to get the .mesh into either .obj or .fbx and then import that into maya.
"If I have seen further it is by standing on the shoulders of giants." Sir Isaac Newton, 1675