The general rule is that the state has jurisdiction over (state) crimes committed on the reservation only when victim and perpetrator are non-Indian. However, in "PL-280 jurisdictions", the state and tribe have jurisdiction in case the perpetrator is Indian, and the state otherwise has jurisdiction. Alaska, California, Minnesota, Nebraska, Oregon, and Wisconsin are the relevant states, and this complexity depends on the specific tribe, see 18 USC 1162. The jurisdiction division applies to crimes committed in "Indian country", which is defined in 18 USC 1151. An Indian (Native American) physician performing an abortion could therefore be safe from prosecution for performing an abortion (as long as there is no federal or tribal prohibition – the Oglala Sioux banned abortion, in response to an earlier proposal to open an abortion clinic). I don't know of a state with a law criminalizing getting an abortion (where there is only a perpetrator), but if there were such a law in a non-PL280 jurisdiction, only Indian women could get an abortion free of the threat of state prosecution. There can also be tribe-specific exceptions, though specific treaty provisions, as discussed here.
A non-trivial impediment to abortions in Indian country is the Hyde Amendment which bans using federal funds to perform an abortion – relevant given the realities of medical care in reservations.