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When I use the knife tool on my mesh, any face connected to the cut becomes "incorrect". (I don't know the true term)

enter image description here

The underside of my mesh was smooth before I cut the mesh. Now, there are odd triangles that even appear in the render.

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    $\begingroup$ Important addition to your question will be screenshots of mesh in Edit mode and stack of modifiers (also a blend file can be useful). Generally there's too much distortion which causes bad shading and artifacts on triangles, most likely topology in that part should be redone. $\endgroup$ – Mr Zak May 7 '16 at 23:14
  • $\begingroup$ Please use the edit link on your post and add more information so that others can help you. $\endgroup$ – cegaton May 8 '16 at 0:31
  • $\begingroup$ We will need before and after pictures of the model in edit mode in order to do more than speculate. $\endgroup$ – Kirbinator May 8 '16 at 2:36
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    $\begingroup$ I'm guessing you created an n-gon in the process of cutting, and now the tris that the n-gon consists of are prevalent in the shading. Try to reshape your topology to quads. Other than that, without seeing the .blend I'm guessing in the dark. $\endgroup$ – Mentalist Mar 9 '17 at 14:15
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Have you tried the J "join" tool instead?

Here is a link to the Blender Reference Manual on Vertex tools

https://www.blender.org/manual/modeling/meshes/editing/vertices.html

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