Can I disable an old security system by disconnecting the transformer?

The wire from the transformer goes into the wall and right back into your alarm panel with the rest of the wires to energize it. Unscrew the wires from the transformer and just tuck them into the wall by the outlet in case you ever want to use the panel again. Tuck the transformer into the alarm box and shut it. There doesn't appear to be any backup batteries but if there are, disconnect them too.

(Mostly) Nevermind - @JACK is right - I missed that this was a plug-in transformer that had been relocated from its normal position. I'm still not thrilled about the cable from it, but you could either tuck it away or pull it out altogether. I'm going to leave most of this here in case it's of use to someone with a "similar but different" install, but it's mostly not applicable to this install with that detail clear.

Well that's an ugly and potentially code-violating install. I can't tell if the cable from below the outlet is from a low-voltage supply bodged to the outside of the outlet and buried in the wall, or is carrying line voltage on low voltage type wire. Neither is "in a workman-like manner" and the latter is downright dangerous.

First: Find the circuit breaker or fuse supplying that outlet and turn it off there.

Then: Pull the outlet and look for "extra wires" - perhaps edit your post with new pictures. I suspect you'll have a pair of wires feeding something attached outside the box (which you can disconnect and cap, making that supply dead and no longer wasting power without having to rip the wall open to get it out), or you'll find the other end of that tiny white cable with red and black wires that should definitely NOT be connected to line voltage. If it is a low voltage supply outside the box, Once the supply wires are disconnected, you can cut the cable off without concern. Pencil in ripping the wall open to remove that thing (if present) next time you plan to repaint in this area.