There are numerous reasons for the Sioux Uprising of 1862. They mainly revolve around the fact that the government was extremely dishonest in their treatment of the Sioux (or Dakota) Indians. The Sioux took it to a point, but it ultimately led to their breaking point.
First off, the Sioux surrendered a numerous part of their land to the whites when they expanded westward into Minnesota. In all they surrendered 28 million acres through different treaties, 21 million of those acres coming from the Traverse des Sioux Treaty of 1851. After all of these treaties were agreed upon, reluctantly by the Sioux, they were left with two reservations for the 7,000 of them that lived in Minnesota. The Sioux reservations are indicated by the broken lines in the map below. They were each only 20 miles by 70 miles.
Now obviously, you would expect the Indians were compensated by the U.S. government for their forfeiture of the land. However, this was not the case. The Indians agreed to purchase goods from the fur traders. They would do this before their government annuities arrived. When the government did come, the fur traders got their hands on the majority of the money. Thus the Indians were left with virtually nothing. This caused a large part of their frustration.
Then their was the fact that the government was rarely on time with their payments. This was especially true in 1862. The Indians were starving in the summer of 1862 and the government was way behind in their annuity payments. Of course, this was occuring at the same time as the Civil War. The Indians weren't stupid. They knew that the majority of the white men of Minnesota were off fighting in the Civil War. So if they did attack they would be fighting a depleted enemy.
All of these reasons led to the Sioux Uprising in the late summer and fall of 1862. The Sioux were being taken for fools by the government and they didn't want to take it anymore.