This phrase often refers to someone who is a rude,
obnoxious or has done something horrible to a person or many people. This is calling them work which we often do not like doing and calling them nasty at the same time, therefore
a nasty peice of something we hate.
"That teenager has
beaten up so many people for no good reason, gosh he is a NASTY
PEICE OF WORK!"
This phrase is often used in first person, for e.g Is a nasty
peice of work, not often Was a nasty peice of work.