Episode S13E22 “Strange Beauty”, aired May 16, 2012 IMDB
A kidnapped young woman turns up dead with an amputated leg, which leads the detectives into the body modification subculture.
Body modification is not the same thing as BDSM, though obviously there is considerable overlap of the two subcultures. The episode of SVU that focuses on body modification deploys a lot of the same tropes as episodes of procedural dramas that focus on BDSM.
Detective Rollins happens to see a woman, Nina, being abducted into a taxi cab. Nina’s mother talks about her distress at seeing her daughter’s extensive tattoos and piercings, which she said started with an octopus tattoo on her ankle.
That’s when a woman’s severed leg with an octopus tattoo turns up in a canal, which leads to another reported severed leg from years ago. The former owner of that leg is a drug-addicted street sex worker who was paid $25,000 by an unidentified john to amputate her leg.