I don't think he "meant to"--I think he so enthusiastically grabbed in his jaws the not-so-bright chipmunk, and that was that. A far faster and more merciful death than a cat might inflict, although with cats (and well-timed human intervention) the chipmunk sometimes manages to get away and live.
So, there we are. A bite of reality about the bite of reality. Poor unsuspecting chipmunk. Not sure why he/she kept making so much of noise calling attention to his/her whereabouts. That's what got Digory interested.
I think Digory was kind of mystified by the whole thing--he set the chippie down on the ground, witnessed its last dying twitches, and then really didn't seem to know what to do. Just kind of sat there by its side, a little hang-dogish. I trust his Corgi-psyche won't be wracked by self-recrimination or shame. He is still and always, fully and only a dog, after all.