When I use the knife tool on my mesh, any face connected to the cut becomes "incorrect". (I don't know the true term)
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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2$\begingroup$ 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
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$\begingroup$ 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
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$\begingroup$ 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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1$\begingroup$ 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
