One method was to cut the tree, let the stump dry out, then burn it. This is known as slash and burn.

Where that was impossible, removing tree stumps was a very labor intensive deal, often requiring neighbors to bring their oxen to help. It seems it was frequently preferred to leave the stumps for years until the roots rotted away, and it could more easily be pulled up.

Here is a photo of a pulley system used to pull up a root.

Philemon Wright, founder of Hull, Quebec, wrote about the process he used in the book "An Account of the First Settlement of the Township of Hull".

In 1815 I employed some men in taking out the small stumps and roots, and levelling of the roughest places as rots began to decay according to the size of the stumps Beech and rock maple stumps are much more readily taken out after the seventh year; pine, elm, basswood, and hemlock are less liable to rot, and therefore require about fifteen years before they can be taken out, especially those of the large size. Every season I set apart a certain number of days, and take from two to six pair of oxen, harnessed with strong chains, which are fastened round the stumps and drawn up, collected together into piles, and burnt upon the ground