You cannot, but see Dragon #271
The Bag of Devouring has been listed as a magic item of dubious value since the first edition of AD&D and has been consistently described in that and subsequent versions, including Pathfinder, as the mouth of an extra dimensional creature. No edition of the rules has included a description of that creature however. Now defunct Dragon Magazine included a long-running series of "Ecology of..." articles, and the bag does receive treatment there according to AD&D 2nd edition rules just months before the release of 3e, on which Pathfinder was based.
Issue #271 of Dragon Magazine, May 2000, includes an article on p. 82 by Kevin Haw entitled "The Ecology of the Bag of Devouring: Hiders Keepers." While the article does specify that the extra dimensional creature is immune to poison, it provides details about the creature, including its combat statistics, which could be used for determining how to kill the creature.
Here are a few details pulled from the article which is presented as a first-person narrative with game mechanics called out as footnotes:
- The interior of the bag is 32" in diameter and 5' deep. [Although for that diameter a 5'4.46" depth is required to yield the DMG-specified 30 cubic feet.]
- The interior is AC 7 [that's AC 13 in Pathfinder terms] and will withstand 15+1d6 points of damage before ripping. If ripped the bag is destroyed, forming a 10-foot-wide vortex to the Astral plan, just as if a portable hole were placed within a bag of holding.
- A devourer launches an acid attack if any damage is inflicted from inside the bag...
The article goes on to include an anatomical diagram of the extra dimensional creature and additional details which I will not reproduce out of respect for copyright and in the interest of preserving some surprise for the players whose DM finds and uses this article.