On Cop, Swans took the style of their previous LP, 1983's Filth, and intensified it, utilising slower tempos, more tape loops and even more abrasive musical textures. The lyrics are again concerned with ambiguous themes like physical, often sexual domination and/or submission. According to Jarboe, who first met the band shortly after this album was recorded, the photograph on the cover is the profile of a morbidly obese woman.
Cop was remastered by Michael Gira in 1992 for release on CD along with the Young GodEP as bonus tracks. The 1999 double disc re-issue Cop/Young God / Greed/Holy Money combines Cop and Young God with the compilation Greed / Holy Money (itself compiled from the albums Greed and Holy Money.) The packaging for all issues states that the recording is "designed to be played at maximum volume".
AllMusic wrote of the album: "Ugly, compelling and overpowering, Cop remains the pinnacle of Swans' brutal early days", calling it "quite possibly one of the darkest recordings ever done.".The Quietus compared the sound of the album to an "open wound".