This expression comes from the getto's of America and it means anyone who tells the police anything will get hurt badly or their family hurt or killed.
Anyone who airs dirty laundry is called a gossip not a snitch.
It literally means that people that tell, even if they report a rape or something truly disgusting, will get stitches (beat to the point of needing stitches) for telling on someone else.
https://en.wiktionary.org/wiki/snitches_get_stitches