The Asphynx is one of two monsters added in SLASH'EM that share the cockatrice's petrification attacks. An asphynx is capable of killing you in the same way a cockatrice is; touching a living or deceased asphynx with an exposed part of your body is instadeath, and the asphynx causes delayed petrification in the same manner as a cockatrice. See the article on the cockatrice for specifics of petrification.
An asphynx is much more dangerous than a cockatrice, as it has more hit dice, lower AC, and is faster than a player without speed. The asphynx is also capable of hiding under items like other snakes, potentially catching the player offguard.
The asphynx is a more dangerous version of a cockatrice and thus should be handled with the same care. The increased difficulty means that they will appear later in the game, preferably late enough for the character to have acquired intrinsic or extrinsic speed. The corpse of an asphynx can be used as a weapon to stone non-petrification resistant monsters (be sure to wear gloves), but the corpse is slightly heavier and the asphynx is both rarer and more difficult to kill, so a cockatrice corpse remains preferable.
SLASH'EM's additional petrifying monsters means that it is no longer possible to avoid potential YASDs by blessed genociding c, as neither the asphynx nor the basilisk are c.
Polymorphing into an asphynx is a better choice for emergency situations than a cockatrice, unless the player is a low level doppelganger. Like a cockatrice an asphynx can lay eggs that will cause stoning, so female players have the option of polymorphing into an asphynx to create future weapons. Alternatively, the eggs could be allowed to hatch; the resulting asphynx will have a higher level than a cockatrice and thus will attack more enemies on its own and have higher hit dice and speed. A pet asphynx will attempt to hide under items, which can be annoying if you do not have a magic whistle.
This small, inoffensive-looking snake shares the feared power
of petrification with its distant relatives the cockatrice and
basilisk. Just one touch from its blunt snout can render one
motionless for all eternity.