slave to the grind means?
it's the album title of skid row
"Grind" likely means in this context the "daily grind", or the routine of going to work every day. This ELU question for example explains this in a bit more detail.
From that question, and from there from dictionary.reference.com:
daily grind (noun)
everyday routine, esp. monotonous
The daily grind was starting to get to her.
So here, Skid Row is referring to being a slave to the daily work routine - either objecting to the fact that you must perform this routine in order to survive, or the fact that once you get in a routine the routine will often control you.