"Thing that turns", from shuutuurrp, "is rolling, turning like a wheel", which comes from transitive shuutuur "makes it turn (like a wheel)".
Kushuutuurrp in Mesa Grande. In Cuevas' version, the sh has become ch (seen in other cases such as the term for "is deaf", where shuupitt may become chuupitt), and the vowel in the last syllable appears to be a short "u". Cuevas also has a pattern of pronouncing a short "r" where other speakers have a long (rolled) "rr".