I recently hit a floating object and it took about a 2" long x 3/4" high chunk out of my skeg. I can have a piece welded in and repainted to have it back to normal.
My question is what would happen if I just cut the skeg straight across, which would shorten the skeg by about 3/4"-1".
Would this affect my performance? Just seeing if anyone has any other suggestions before I fix this.

You can just use JB Weld, sand and repaint. It will be as good as new. I know of lots of people who have done this, including myself and have never had the piece come out. Cheap and easy.

If you cut the skeg down you should gain some speed, but it may not be noticeable. You won't have prop protection from foreign objects. Your steering may be effected, depending on the hull, you may swap ends on a tight turn, not good!

Mercury and others make replacement skegs if yours is too far gone.

Max V, Have you considered skeg guards? They are
stainless steel & slip right over the existing skeg. You
just drill 2 holes and install the special bolts supplied.
Takes 10 minutes,looks trick and contrary to belief,you don't loose any speed. Overtons sells them for about
$100.00 I've got them and have had no problems.
Rick

Max if your drive is deep in the water you can cut 1''-2'' off with no problem. If your drives are high you may have problems. But you need to weld on them anyhow so cut it off and if you don't like it have a new piece welded on. It will be no more work.