David Wells Kilbourne gives us one of the earliest anti-Mormon accounts of the death of Joseph Smith in a letter written just two days after the fact from Fort Madison to an Anglican parson named Thomas Dent who lived in England and was curious about learning more. Kilbourne was staying at the Nauvoo Mansion House - which he calls "Joe's tavern" - at the time when news arrived in Nauvoo. Here is the essence of what Kilbourne wrote to Dent:
I hasten to inform you of the wonderful events which have taken place at Nauvoo since my letter to you a few days since. The work of death has been commenced. The Mormon Prophet Joe Smith & his brother Hyrum are no more. I have just returned from Nauvoo & I this day looked upon the lifeless remains of these two men - the great heads & leaders of Mormonism. Their work of infamy is finished & their dupes about two hours since committed their remains to a silent grave. But I will hasten to give you the particulars as full as I am able in a single letter.....
On Thursday morning 27 [...] In the absence of the Gov. & about 4 O Clock P.M. of this Thursday 27th day of June, an armed and disguished band of men, about two hundred in number attacked the Jail - overpowered the guard of eight men, entered the Jail and shot both the Smiths. Hyram received a ball in the head, and mearly had time to exclaim "I am a dead man," and expired; Joe received a number of balls which pierced his body, some while still in the Jail, some while he was in the act of leaping from the window of the Jail, and others after he reached the ground, he exclaimed "O God" - and expired.
Elder Taylor who was also in the jail received several flesh wounds, is considered dangerous. The disguished band immediately escaped to the woods & were not pursued for want of force sufficient to take them. They were all disguished with paint, & of course not known.
There is but one feeling throughout this country in regard to this last tragedy, & that is, that merited vengeance had fallen on the right men, at the same time all regret that it happened while he was a prisoner & had a right to expect protection. It is regretted because his followers will now claim that he died a martyr when if he could have been tried on the charges & convicted he would have died a felon.
This is taken from Warren A. Jennings, "The Lynching of an American Prophet", BYU Studies 40/1 (2001): 207, 209-210. I thoroughly recommend reading the article, which contains three of Kilbourne's letters to Dent.