Again, opinions vary, and several different methods seem to work well for different people.
Keep in mind that if you pull on the caps or their leads before the solder is fully melted, you could lift the copper pad to which they are soldered from the circuit board. This is bad, though not completely catastrophic.
If you use the cutting method, be careful, and gentle, and make sure you don't lift on the cap while cutting, nor bend it over, or otherwise apply lifting, bending, twisting, torquing force to it which could lift the underlying pad.
Once the cap can is cut off it is relatively easy to desolder the pins one at a time.
My preferred method is to use two soldering pencils simultaneously and just heat both leads util the cap comes off. This has its own hazards, as if the solder does not melt quickly, sometimes folks get impatient and either grind the solder pencil tip(s) into the pad, damaging it, or they use the two pencils like tweezers and try to pull the cap off before the solder is melted.
But with patience, the two pencil method seems the least hazardous to me.
Every method requires patience and an awareness that applying the wrong force could be damaging.