Go to your Steam Library, right click on Garry's Mod and hit properties. Under one of the sections is "Set launch options". Click that and type (-dxlevel 91) exactly how that it without the parenthesis. If that does not work, try 95 also. Overall, try numbers between 91-99, and see what works for you. I had this problem and I had to figure it out on my own, so I'm hoping this works for you, otherwise, PM me and I'll see what I can find on how to help out.
EDIT: I thought I would explain this so people can know what it means. One of Gmod's components or programs (whatever you call it) it uses to run is called DirectX. By default, Gmod usually uses some version of DirectX 8. Changing the dxlevel (DirectX level) changes what version Gmod will use. The top 3 I have found are dxlevel 100, dxlevel 91, and dxlevel 95. Most of the time these will work.