They Bite by Anthony Boucher
Story is out of copyright and can be read online here
A man was turned down for enlistment in the army due to his lungs. He decides to do something about it by moving into the desert. But he keeps seeing something like an animal out of the corner of his eyes.
The locals tell him to stay away from the adobe brick hut. When pressed all they will add is "They bite"
He investigates the adobe anyway, because it will be cool in the desert heat.
He is amused to discover what looks like the mummified body of a child. His amusement turns to horror when he notices that it is breathing.
Suddenly a second such creature walks in the door. It jumps at him and latches on to his hand with its jaws. In agony, the man uses a machete to decapitate the creature. But the head is still attached and the pain continues. Attempts to pry the jaws open are fruitless.
So the man uses the machete to chop his own hand off.