Excellent question!
I've addressed that several times on FR threads -- including one from 3.5 years ago: Mormon Times [The Mormon Times is no longer published as such, but owned by the Mormon Church]: 'A different take on the Carthage mob -- BYU Studies Symposium' [see especially post #2...which I've recopied below].
From all indicators, one bullet likely (accidentally) went into his brother Hyrum's back...but was not the fatal shot that killed Hyrum, which came from the front.
Note this source: Official History of the Church (Vol. 7, pp 100-103):
"I shall never forget the deep feeling of sympathy and regard manifested in the countenance of Brother Joseph as he drew nigh to Hyrum, and, leaning over him, exclaimed, 'Oh! my poor, dear brother Hyrum!' He, however, instantly arose, and with a firm, quick step, and a determined expression of countenance, approached the door, and pulling the six-shooter left by Brother Wheelock from his pocket, opened the door slightly, and snapped the pistol six successive times; only three of the barrels, however, were discharged. I afterwards understood that two or three were wounded by these discharges, two of whom, I am informed, died."
And: "It certainly was a terrible scene: streams of fire as thick as my arm passed by me as these men fired, and, unarmed as we were, it looked like certain death. I remember feeling as though my time had come, but I do not know when, in any critical position, I was more calm, unruffled, energetic, and acted with more promptness and decision. It certainly was far from pleasant to be so near the muzzles of those firearms as they belched forth their liquid flames and deadly balls. While I was engaged in parrying the guns, Brother Joseph said, 'That's right, Brother Taylor, parry them off as well as you can.' These were the last words I ever heard him speak on earth."
From two other sources, as cited by Tangible Information:
Reporter John Hay, of the Atlantic Monthly identified three men who were shot by Joseph Smith:
John Wills in the arm,
William Vorhees in the shoulder,
and William Gallagher in the face.
Hay was a son of Charles Hay, a surgeon of the Carthage militia and apparently a member of the mob.
"Smith had two loaded six-barrelled revolvers in his room. How a man on trial for capital offences came to be supplied with such luxuries is a mystery that perhaps only one man could fully have solved; and as General Deming, the Jack-Mormon sheriff, died soon after, and left no explanation of the matter, investigation is effectually baffled. But the four shots which I have chronicled, and two which had no billet, exhausted one pistol, and the enemy gave Smith no time to use the other. Severely wounded as he was, he ran to the window, which was open to receive the fresh June air, and half leaped, half fell, into the jail yard below." - John Hay, "The Mormon Prophet's Tragedy," Atlantic Monthly (December 1869) 671-678.
The same Web site says:
In another contemporary account from a faithful Latter-Day Saint: "Of the three barrels discharged by Joseph, it is believed he hit three men:
an Irishman named Wells-who was in the mob from his love of a brawl-in the arm;
Voorhees-an oversized kid from Bear Creek known for his lack of good sense-in the shoulder;
and a man named Gallagher-a Southerner from the Mississippi Bottom-in the face."
"Two other men were known to get hit in the hall, one a man named Townsend from Fort Madison, Iowa Territory, who died nine months later from the arm wound that wouldn't heal,
and another named Mills, who was shot in the arm." - Elder Reed Blake, 24 Hours to Martyrdom, p. 129
So as these mob members were shot down by Joseph Smith and perhaps another left standing in room, how is it that Joseph's brother, Hyrum, came to have a back wound?
From a Mormon author:
Very interesting times to be sure.
Some of the mob people shot could have been shot by other members of the mob.
forensics at that time were pretty primitive. Certainly Smith should not have been armed if in jail. I read, some years ago an account that had Hyrum outside the jail, trying to escape, with Joseph following. Can’t find it now, and that is contradicted by many (Mormon)sites.
Also lost to history is who fired first. It was asserted that Hyrum was shot in the face as someone attempted to open the door by shooting the lock, but that is a very unlikely method of opening a lock, and penetration through the lock would be unlikely.
In addition to not being very good at fraud, or banking, I would suggest that Joseph was not very good with a pistol.