I have cut a cylinder that I put into a conic shape with the knife too.
I want to remove the lower part but cannot select it.
Whatever I do, the whole object is selected.
If I try any selection it never selects the backside of the object, not the front side?
What would be the best way to select half of an object cut in half with the knife tool?
Thanks!
Turning on X ray mode might help (Alt Z) 
I’m struggling to visualize your exact scenario, could you share a screenshot?
Select the object, go into edit mode, toggle X-Ray on. Pick the Select Mode – vertices, edges, or faces – drag the Select Box over the parts you want to select (or the Circle or the Lasso select, they all work the same).
The x-ray is what does the trick here, but you can’t turn it on in Object mode (which annoys me to no end even though it makes sense).
you can also quickly switch to wireframe in order to select through faces, if potentially that is more your jam.
PROBLEM: When I select with the brush the vertices get selected PAST THE CUTTING LINE and again I cannot select the lower part of the object.
PS:
Is there a way, e.g. select the cutting line?
and then ctrl + - to select everything beneath the cutting line so I don’t have to paint every part of the object I want to delete?
If your object is symmetrical across an axis, you can cut half of it away and then put a mirror modifier on the remainder, that way everything you do to that will be reflected across that axis. You can reflect across more than one axis at once.
