First, mice don't need meat to eat.
Second, deli meats are super high in salt, and thus not a healthy thing to be feeding rodents.
I used to give my rodents the leftover chicken "bones" with the bits of meat on them after *I* ate chicken. Most "leftover" meats you could probably give them, but again... mice don't need meat and it might be detrimental to their diet to give them much.
Theresa Baker
No Legs and More
Florida, USA
"Stop being a wimpy monkey,; bare some teeth, steal some food and fling poo with the alphas. "
Yup, meat is not necessary, but if you're the type that really hates to waste or throw out anything, scraps and bones (cooked of course) from your leftovers are OK. They do seem to enjoy the workout their teeth get from chewing on rib bones or chicken bones.