something torn off particularly with one’s hand; rip, tear, or snag
# Fragment: a piece that has been broken or torn off from something larger.
# Shred (n) a long, thin piece that has been torn or cut off from something.
# Tear (v) the act of pulling or ripping something apart, and it can also be used as a noun to describe a rip or a tear in something.
However, the most specific and commonly used lexeme to describe "a piece torn off from something" or "to tear off" is probably:
# Ripped/Rip
This verb can be used to describe the act of tearing or pulling something apart, and it can also be used as a noun to describe a tear or a rip in something.
# Snapped/Snap
This verb can be used to describe the act of breaking or tearing something suddenly, and it can also be used as a noun to describe a sudden break or tear.
# Scissors' snip isn't the only way something can break off; things can also be torn.
The word 'snippet' usually means something deliberately cut, while something torn off can be described with words like shred, rip, tear, or snag.