I was circumcised as a baby, but somehow a small piece of skin is still attached to my penis. Should I cut the skin off?

No. Unless the skin is painful or tears with erections or stimulation, i would suggest doing nothing.
Yes if U R a surgeon. Otherwise let a doctor, urologist or surgeon remove it.
Should YOU? No. This is not a procedure (nor a work area) for do-it-yourselfers. A little piece of foreskin is not going to get in your way or otherwise cause you any inconvenience, so there is no need to do anything. If you find it unacceptable cosmetically, let a doctor remove it, please!
Save it for kitchen. This is not uncommon. If you want to do some DIY activities you should save it for those renovations around the house. At least there you can call someone in on a non urgent basis if you mess up. Here you can trigger an infection or serious bleeding that could permanently scar your friend. Either leave it alone or have someone that does that for a living decide what should be done.