IIRC, in my old home state of Oklahoma, deer can be taken by means of bow/arrow, crossbow (for
archers with physical challenges), blackpowder rifle, shotgun (with slugs and
maybe also with "buckshot") and rifle.
(I suspect that high-powered pistols, such as .357 Mag, .44 Mag, or chambered for
high-powered rounds, like with the Thompson Contender Pistol might also be legal).
One year the biggest buck taken in the state was brought down by a young boy (early teen?)
with a single shotgun slug at a range of about 30 yards.
One more reason to be glad I live in Colorado.
Shotgun deer hunting may be legal here too for all I know but hunters here tend to lean toward a 30.06 to do the job or at least they used to when I was around them.
Distances are long. You aren't likely to get within 30 yds. of a muledeer in hunting season.