A statue gargoyle is a new, somewhat weaker variant of a gargoyle in SLASH'EM. It is distinctive because it will very likely be the first monster the player encounters with the SLASH'EM-distinctive property "need +1 weapon to hit." A pick-axe type weapon will bypass this requirement and seems to destroy the Statue Gargoyle instantly.
The enchantment resistance can be a vexing property if your character does not possess a pick-axe type weapon, especially since pets that don't possess the "hits creatures as a +1 (or greater) weapon" property will not be able to harm it either, unless they are wielding a sufficiently enchanted weapon. This includes all domestic animals, and in fact most monsters that are not in some way magical. Note that for the purposes of the enchantment check, if a weapon is an artifact weapon, it gives +2 to that check. In the case of the statue gargoyle, any artifact weapon will thus harm it if its enchantment is greater than -2.
Casting stone-to-flesh on a statue gargoyle will turn it into a normal gargoyle, which can be destroyed with an unenchanted weapon. However, since normal gargoyles are far stronger and better armored than statue gargoyles, it is probably easier to leave the statue gargoyle alone until you can find an enchanted or artifact weapon. Statue gargoyles do possess two attacks; however, neither is particularly strong, and they are not particularly fast, and so retreat is always an option. Oddly enough, although attacks with an insufficiently enchanted weapon will do no damage to a statue gargoyle, it will increase your skill counter, making it possible to use them to train skills indefinitely, provided you have sufficient AC to survive their attacks.