Kato,

I have a wall outlet located near the ceiling (probably for a clock)
that I'd like to remove and then patch over. This outlet is on the
same circuit as another outlet near the floor that I want to leave in
place. My question: Can I just remove the box, connect the wires on
both sides from this top outlet, then cap off and tape these wires and
leave them in the wall before I patch over the hole?

If the outlet is near the ceiling, and this is in a bedroom, it might be
for a smoke alarm? If so, you should probably install a new smoke alarm
there.

Otherwise, if there is only the one cable entering the box, and you can
disconnect the power supply on the opposite end (with no chance of
reattachment), there's no reason why you couldn't take out the box and
leave the old wiring in the wall. It's done all the time when old wiring is
updated.

HOWEVER, if you have other cables connecting in the box, you can't just
bury the box. The connections have to remain accessable. Just use a blank
cover plate and paint it to match the wall.

If you REALLY want to remove the box, you'll need to find where those
cables go, then route a new single cable from source to destination.
Eliminate the cables in the box, then you can eliminate the box.

Anthony