Unlike most commonly-kept snakes, garter snakes won't always adapt to taking dead mice - though some will.
Garter snakes rarely grow to a body diameter large enough to cope with adult mice as food though some specimens will, with time, learn to take pinkies or fuzzies.
I have even seen breeders charging more for those garter snakes that will take pinkies because it makes the new owners life so much easier in the long run and is a worthwhile investment.
Otherwise garter snakes will take a range of other food in captivity.
For example, if placed in a bowl so they don't disappear in the substrate, earthworms can make suitable garter snake food as will a range of fish.
This may take the form of small live fish sold as pets in the aquarium trade - such as goldfish or minnows - or pieces of dead fish bought from a fishmongers.
If you decide to do this ensure they are untreated (not smoked, colored etc.) and if you decide to feed fish as garter snake food at all make certain you're using a good quality supplement.
This is because history has shown that some fish is high in an enzyme called thiaminase which can lead to vitamin B deficiencies in garter snakes.
Over long periods of time this deficiency can result in such symptoms as fits, paralysis or even death.
Lastly, when discussing garter snake food, there are several specialist, "processed" garter snake foods which provide all nutrients necessary in a practical (if expensive) form.