His paternal grandparents were Captain Richard Alsop and Hannah Underhill (1666–1757), who first settled in New York during the 1650s and served as a major in Oliver Cromwell's army, but after a disagreement with the Lord Protector, he fled to the obscurity of colonial life.

[3] As a young man he moved to New York City and entered the mercantile world with his brother Richard.

In 1774, Alsop, along with James Duane, John Jay, Philip Livingston, and Isaac Low, was named as a delegate.

[11] As the revolution escalated in 1775, Alsop was one of the leaders of the Committee of Sixty which became the provisional government in New York City.

[12][13] Alsop favored reconciliation with Great Britain and so resigned as a delegate to the Congress rather than sign the Declaration of Independence.

He made several trips between there and New York, acting as an agent of Congress through his business to acquire supplies, and particularly powder for the Continental Army.

After General Washington visited Congress in late May, Alsop returned with him to New York in early June.

[14] He added efforts to find housing for 8,000 Continental Army troops to his earlier and continuing work on the supply problems.

[18] Alsop died at his home in Newtown, Queens County, New York, on November 22, 1794, and is buried in Trinity Church Cemetery in Manhattan.