A thief in the night cleanly amputated two arms off my 4 ft (1.2 m) tall cactus. What do I do?
The cut part cannot regrow a top to look like it was before, but the remaining portion of the arm can make more arms and continue growing that way.
Depending on your climate, it may take a few days or a few weeks for the wound to dry out and form a callus. If you think it'll take a while to dry out, you can dust it with some anti-fungal powder (commonly available at nurseries) so that the wound doesn't get infected. Some people have luck using cinnamon as a fungicide, but I have not tried it.
What angle was the cut made? If it's just a flat cut straight across, it will allow water to collect during rain. Standing water on a cactus can lead to rot, so you might want to cut it at an angle to allow water to run off.
As others have mentioned, photos of your cactus would be very helpful. You might be able to remove the entire arm and re-plant it if you find the injuries on the original cactus aesthetically unpleasing, but photos would help us give advice for your case.