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1.
A term used among the deer hunting community to describe an amateurish or other wise incompetent hunter who, through carelessness or lack of skill, shoots his deer directly in the ass instead of the vitals. These so-called hunters usually demonstrate the act on immature bucks or small does as these animals are easy game even for novice hunters. Luckily, big bucks seldom fall victim to this type of incompetence due to the fact they easily outsmart these neophyte hunters.

The phrase is derived from novice hunters acting like 'cowboys' in the woods, shooting without aiming, taking risky shots and posing other hazards, ultimately wounding deer with the dreaded 'texas heart shot'.
Man #1: Anybody have any luck at your hunting camp yet?

Man #2: No but Jeff has taken a few texas heart shots!

Man #1: Man, what's that guys problem????
by The Gov'nor July 23, 2013
 
2.
Cumming in one's asshole during anal sex
Paul delivered a brutal Texas Heart Shot on Anna's cow.
by Arab Bastard January 14, 2007