There are 2 drawbacks I see to this:
1- this would require at least 2 hands to use, so may not work for self-aid,
2- because of contamination issues with the water filter, This should probably only be done for a life-threatening snakebite or scorpion bite, and not for more minor insect stings that the sawyer could potentially be used for.
There is another drawback. Suction doesn't work (I know that sucks). At least that is my understanding. Case studies show that suction is ineffective. The best course is to remain as immobile as possible and get to an ER (contradictory, I know). Most snakebites are not life-threatening; scorpion stings are even less so - the only fatalities I know of were to very young children.
If you use even minimal precautions (avoid placing your hands and feet in areas you can't see) and you are not deliberately messing with the critters, your chances of being struck by lightning exceed those of being snake bitten.