I use a hand-operated can opener, and usually open the can about 90 percent and pour out the contents so that the lid doesn't splash down.
Should I continue cranking until the lid separates, and throw the lid away?
Or should I leave the lid attached and carefully bend it back so that no sharp edges protrude?
Both lid-opening options are fine for recycling metal cans. But, please give us the lid in either case. If you cut the lid off completely, the safest thing is to tuck it inside the can, and to gently pinch the can's opening to trap the lid inside. Then, put the can into your blue bin for collection.