The use of force (up to and including the use of deadly force) is one of the many things covered in the Texas Concealed Handgun License class. As mentioned, the laws are going to vary by state, so I can only speak for Texas here.
Basically, you can use the threat of force if you could actually use force in the situation.
To use force, the actor must reasonably believe force is immediately necessary to avoid imminent harm. In self defense, one is not justified by using force in response to verbal provocation alone, to resist a peace officer making a lawful arrest, if the actor consented or if the actor provoked the use of force (unless the actor abandons the encounter or indicates his intent to abandon the encounter.)
To use deadly force, the actor is justified if: he is justified in using force, as above, and if he reasonably believes the deadly force is immediately necessary to a) protect himself from the other’s use or attempted use of unlawful deadly force, or b) to prevent the other’s imminent commission of aggravated kidnapping, murder, sexual assault, aggravated sexual assault, robbery, or aggravated robbery.
It should be noted that the law used to mandate that the actor had a duty to retreat, if a reasonable person would have done so. That changed in the last legislative session, which struck the duty to retreat (resulting in Texas being a “castle doctrine” state.)
Deadly force can also be used in defense of a third person, if the actor reasonably believes he would be justified in using deadly force to protect himself in that situation, and believes that his intervention is immediately necessary to protect the third person.
Finally, force and/or deadly force can be used to protect property. Deadly force is justified when the actor reasonably believes the use is immediately necessary to prevent the other’s commission of arson, burglary, robbery, aggravated robbery, theft during the nighttime, or to prevent the other who is fleeing immediately after committing burglary, robbery, aggravated robbery, or theft during the nighttime and is escaping with property that cannot be protected or recovered by any other means. The actor must also reasonably believe that a lesser use of force would result in substantial risk of death or serious bodily injury.
In the OP, I’d say that once the initial encounter was over (the security dude had grabbed the bag, regardless of whether it drew blood or not) the risk of serious bodily injury was over. Using force against the security dude after that was not justified - both parties were guilty of assault, and possibly battery.
In a split-second, fight-or-flight situation, one cannot be thinking about the legalese, so to boil it down to essentials: in Texas, one can use force to prevent immediate harm; one can use deadly force if one would be justified to use force, and reasonably believes that using deadly force will prevent death or serious bodily injury of himself or a third party.