What was the real reason the press was declared a nuisance? In my opinion, the paper was declared a nuisance because it exposed Joseph Smith's private doctrine and practice of polygamy. You can read the Nauvoo Expositor [pdf-file] and decide for yourself.

The order that Joseph Smith gave certainly went beyond "removing" the nuisance, in my opinion. The order said:

To the Marshall of said City, greeting.

You are here commanded to destroy the printing press from whence issues the Nauvoo Expositor, and pi the type of said printing establishment; and if any resistance be offered to your execution of this order by the owners or others, demolish the house; and if anyone threatens you or the Mayor or the officers of the city, arrest who threaten you, and fail not to execute this order without delay, and make due return hereon.


By Order of the City Council,
Joseph Smith, Mayor (History of the Church, vol. 6, page 448)

Within a couple of hours of Joseph's order the press was destroyed. Accounts of the event indicate that it was attended by a very large number of people and that the press went through the window of the building.

Vilate Kimball ltr 7 Jun 1844 in Helen Whitney, WE 11 (1882), p.106
June 11th. Nauvoo was a scene of excitement last night. Some hundreds of the brethren turned out and burned the printing press of the opposite party. This was done by order of the City Council. They had only published one paper (Nauvoo Expositor) which is considered a public nuisance. They have sworn vengeance, and no doubt they will have it."

Mosiah Hancock Autobiography, typescript, BYU-S, p.25 - p.26
The newspaper, "The Nauvoo Expositor", was printed and issued by the spawn of Satan. They printed the most abominable lies and misrepresentations. These falsehoods were more than the Prophet and the good Brethren could stand. One night, I had a notice that something was to be done by the despisers of iniquity. I shouldered my rifle and marched along, and I saw the press and type go through the window. I picked up a hat full of type, shouldered a press log, and with my rifle returned home, arriving there about 4 o'clock in the morning. Right or wrong, I thought I was prompted to do it, but from that time on, all the powers of the evil one seemed to be directed against the Prophet. He knew no peace from then until his death. Some may ask why I did it; and as I said, Right or wrong, I think that I was prompted to do it. The heavenly watchers know more about it than I; and the Power of Heaven did the prompting.