The usual method of forest clearance on the New England frontier in early colonial times in America (1630-1800) was to start by girdling the bark on the trees so they would die.

Girdling meant to cut a ring of bark off all around the trunk of the tree. This kills the tree.

A settler could crop corn and beans among the girdled trees once they produced no leaves to block the sunlight.

The dead trees would then be felled over time (usually felled with axes, the stumps and roots grubbed up by digging and hauling with ox teams) , with some used to build housing, the better ones taken to the sawmill to be turned into lumber, and the remainder and the roots burned down into potash, which was a valuable cash crop, exported to England to be made into soap.

The early years of a New England forest farm were often the most prosperous. The soil was still rich, and produced good crops, there was significant extra income from lumber and potash, and the cleared hillsides could be sown in English grasses and used to graze cattle and sheep. (Though sheep only became viable once a territory was settled enough to have hunted out all the wolves.)

Early New England was covered with forest, and had an extreme shortage of grass. The native American grasses in New England, found in coastal marshes and river terraces, were inferior grazing for farm animals compared to European grasses. This meant that it was difficult for the colonists to raise animals. Their solution was to clear the forests and plant the uplands with English grasses.

Livestock were even more valuable than crops on remote farms, because they could transport themselves to market.

Generally, on the New England frontiers, the settler and his family would clear the forest and burn the potash. In the very early days, the good logs would be sawn into boards with pit saws, and this might involve help from the neighbors. Later, the logs would be sent to a local sawmill, powered by a water wheel, to be cut into lumber.

Shaping lumber into barrel staves, and cutting cedar shake shingles, could also be done by the settler, but were more often done by the lumber mill in later colonial times.

So, on the New England frontier, a settler would clear the land gradually, over time, but would girdle and kill the trees much more quickly and over larger areas than the areas where the dead trees would be felled and turned into useful products.

References:

McManis, Douglas (1975). Colonial New England, A Historical Geography. New York: Oxford University Press.

Bieran, Paul (2005). Clearcutting and Erosion in New England, The Photographic and Stratigraphic Record, Retrieved from Vignettes, Key Concepts in Geomorphology, at http://serc.carleton.edu/vignettes/collection/24682.html

One way how to clear land was the slash-and-burn method.

The other way was clearcutting with grubbing - removal of stubs. That could be done with an axe, saw and a team (of oxen or horses). They cleared as much land as they could till that year.