You’re using Shift-K, right?
You can minimize the amount of damage done by first selecting only those faces you wish to cut. However, adjacent faces will also be subdivided to accomodate the new vertex(es). This is a deliberate design decision to avoid ray errors (like seeing light from under the door because the door is not attached to the floor but only the frame).
If you really want to get around it, first select the adjacent faces that you don’t want subdivided, and press X --> Only Faces. After you’re done cutting, you can select the vertices of the faces you deleted and press F to replace them. (Don’t forget to use Ctrl-N to recalculate normals when you’re done!)
Hope this helps.