The bum seizing control of the cart is robbery because he appropriated the OP's property and made a verbal threat. This justifies deadly force, which in turn allows for a threat of deadly force, verbal or otherwise to create an apprehension that you will use deadly force if necessary (i.e. "ill shoot you in the face" or clearing leather).
The part where it gets tricky is the interpretation of 9.42.3.A - you reasonably believe the land or property cannot be protected or recovered by any other means; and 9.42.3.B - you reasonably believe the use of force other than deadly force to protect or recover the land or property would expose the actor or another to a substantial risk of death or serious bodily injury.
Personally, I would not have shot the man over some groceries, but depending on the outcome of a quick verbal threat, I would feel legally comfortable drawing down on the man to let him know I mean business.
Again, IANAL, but this was more than a verbal "gimme some cash." The bum took control of the OP's property forcibly. The OP did a good job IMO.
Just my .02 cents.
Sec. 31.01
(4) "Appropriate" means:
(A) to bring about a transfer or purported transfer of title to or other nonpossessory interest in property, whether to the actor or another; or
(B) to acquire or otherwise exercise control over property other than real property.
Sec. 31.03. THEFT.
(a) A person commits an offense if he unlawfully appropriates property with intent to deprive the owner of property.
(b) Appropriation of property is unlawful if:
(1) it is without the owner's effective consent;
Sec. 29.02. ROBBERY.
(a) A person commits an offense if, in the course of committing theft as defined in Chapter 31 and with intent to obtain or maintain control of the property, he:
(1) intentionally, knowingly, or recklessly causes bodily injury to another; or
(2) intentionally or knowingly threatens or places another in fear of imminent bodily injury or death.
(b) An offense under this section is a felony of the second degree.
Sec. 9.42. DEADLY FORCE TO PROTECT PROPERTY.
A person is justified in using deadly force against another to protect land or tangible, movable property:
(1) if he would be justified in using force against the other under Section 9.41; and
(2) when and to the degree he reasonably believes the deadly force is immediately necessary:
(A) to prevent the other's imminent commission of arson, burglary, robbery, aggravated robbery, theft during the nighttime, or criminal mischief during the nighttime; or
(B) to prevent the other who is fleeing immediately after committing burglary, robbery, aggravated robbery, or theft during the nighttime from escaping with the property; and
(3) he reasonably believes that:
(A) the land or property cannot be protected or recovered by any other means; or
(B) the use of force other than deadly force to protect or recover the land or property would expose the actor or another to a substantial risk of death or serious bodily injury.
Sec. 9.04. THREATS AS JUSTIFIABLE FORCE. The threat of force is justified when the use of force is justified by this chapter. For purposes of this section, a threat to cause death or serious bodily injury by the production of a weapon or otherwise, as long as the actor's purpose is limited to creating an apprehension that he will use deadly force if necessary, does not constitute the use of deadly force.