When I do this I usually use the RenderTarget2D class, drawing the separate areas to rendertargets first and then drawing the rendertargets to the screen. However it seems this can also be done with the ViewPort class as well.
A similar topic discussing this can be found here:
Also an example using Viewports can be found here (the XNA download might not work with MonoGame but the explanation and code should still be applicable):
http://rbwhitaker.wikidot.com/viewports-split-screen