Render to a render target and use
Texture2D.GetData then save the data or use
Texture2D.SaveToJpeg. I have a PR up to implement
GraphicsDevice.GetBackBufferData so you can get texture data directly from the back buffer, but that's currently not implemented in the develop version.
Alternatively you can use reflection to get the DX handle (assuming DX is the backed you're using) and go from there. You can check MonoGame source code to see how to get it. This is not cross platform though, and it's easier to let MG do the heavy lifting.