[citation needed] Common names include acacia bush, catclaw acacia, catclaw mesquite, Gregg's catclaw, paradise flower, wait-a-minute bush, and wait-a-bit tree; these names mostly come from the fact that the tree has numerous hooked prickles with the shape and size of a cat's claw which tend to hook onto passers-by; the hooked person must stop ("wait a minute") to remove the prickles carefully to avoid injury or shredded clothing.

(The common name "cat's claw" is also used to refer to several other plant species, including Uncaria tomentosa, a woody vine found in the tropical jungles of South and Central America.)

The specific epithet greggii refers to Josiah Gregg, a 19th-century author, explorer, and amateur naturalist of the American Southwest and northern Mexico.

The fruit is a flat, twisted legume (pod) 6–15 cm (2.4–5.9 in) long, containing generally 3 to 5 hard, flattened, medium brown seeds.

This effectively prevents germination unless a flash flood disturbs the area and deposits enough water to increase the likelihood that seedlings will be able to establish deep enough roots to survive the dry season.

A tentative connection has been made between these glands and insects that would suggest a mutualistic relationship (as found in other Senegalia species).

The young, unripe beans of S. greggii were gathered and eaten by desert tribes of North America, including the Chemehuevi of the Southern Paiute, the Pima, and the Cahuilla.

The sticks were also used to dislodge saguaro fruits from the cactus body, and rods were curved to flesh animal skins.