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 and decide for yourself.
The order that Joseph Smith gave certainly went beyond "removing" the nuisance, in my opinion. The order said:
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.
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.
The destruction of the Nauvoo Expositor printing press was certainly wrong. Although Elder Dallin H. Oaks believes that the destruction of the newspaper was within the law, he admits that destroying the press went beyond the law:
"The characterization of the printing press as a nuisance, and its subsequent destruction, is another matter. The common law authorities on nuisance abatement generally, and especially those on summary abatement, were emphatic in declaring that abatement must be limited by the necessities of the case, and that no wanton or unnecessary destruction of property could be permitted. A party guilty of excess was liable in damages for trespass to the party injured.... there was no legal justification in 1844 for the destruction of the Expositor press as a nuisance. Its libelous, provocative, and perhaps obscene output may well have been a public and a private nuisance, but the evil article was not the press itself but the way in which it was being used. Consequently, those who caused or accomplished its destruction were liable for money damages in an action of trespass." (Utah Law Review, Summer 1965, pages 890-891)