Yes, you can do that if you know what your are doing and realize it may be the mix, or you planted it too soon after you got the cutting. If you have high humidity that may rot it as well, if you did let it dry out long enough before watering it again, it needs far more light then you are giveing it or the top would not get pointed. It actually should have roots showing before planting, or watering. Cut off and set it in a shallow pot, set aside out side in the shade or lay it down so it gets a lot of air circulation until it roots. Just because I don't grow many cactus doesn't mean I don't have a few and don't know how, I propagated for the Huntington for about 18 years, it's lots of fun. Norma

I'd slice you a new piece that is completely healthy; at least six inches long is a nice size. Let it callus for a couple weeks out of the sun, but outside. I'd use a plastic pot maybe an inch or so bigger in diameter than the base of your cutting. Fill the bottom half of the pot with some cactus soil, stick your cutting on top of the soil, then put a couple or 3 inches of pea gravel around the cactus and on top of the soil. Mist it regularly. It should root eventually but it might take some time and I would not be trying to root it in an office. Fresh air, bright natural light is better. If your plastic pot is unstable, put it in a bigger terra cotta pot and stuff newspaper around the plastic pot to make it stable. Although in this case the gravel should give you weight and you might not need to do this, this is not a bad idea to avoid accidental upheavals.
In nature these columnar cacti fall over and lay on the ground. Over time new columns shoot up off the old column. Doesn't sound like you have a long enough column to try this, but you can see how it works and how much these want to root and grow without any human help.
Some guy was trying to sell 5 foot sections of these on the local craigslist for 75 bucks each! Dream on.
Anyways I have rooted cuttings of san pedros as described above. Good luck.