Thug portion of "thuggapunk" relates to their incessant use of ebonics and offensive slang.
Punk portion applies to their use of safety pins and dyed or spiked hair.
Usually Hot Topic kids with white trashy backgrounds. Seen often with the hatchetman on chains around their necks, safety pins lacing their black clothing (read: everywhere) and bad senses of style. Often they call themselves juggalos and juggalettes.