Question:
Why could George Washington and the revolutionaries not stop Governor Tryon in New York Harbor?
Short Answer
The Patriots were divided into factions. The more radical factions wanted to arrest Governor Tryon, but the more moderate faction in this case lead by George Washington basically stopped them. Washington was waiting on the Continental Congress to clearly authorize the war before he was going to take the provocative step of arresting a British Hero and Governor of NY. Tyron fled to the British ship Halifax in Oct 1775. George Washington didn't get his "authorization" from congress until July 4, 1776 in the Declaration of Independence.
Detailed Answer
The question shouldn't be whether the revolutionaries could stop Governor Tryon in New York prior to October 19, 1775 when he fled into the harbor. The question should be why they didn't.
Governor Tryon had just returned from England June 25, 1775, In July of 1775, the Continental Congress had issued orders to Isaac Sears for the arrest of Governor Tryon.
George Washington who had just been appointed the Commander and Chief of the Continental Army (June 19, 1775) interceded and commanded Issac Sears to stand down.
First Who was Governor Tryon... Tryon was a former British General who had been the Governor North Carolina for six years (1765 to 1771.) during the War of Regulation. He was known to many patriots as a brutal and oppressive British official, while known to the British as a hero who had already put down one colonial rebellion.
Who was Isaac Sears a privateer from the French and Indian War, who nursed a personal grievance against the British since the Sugar and Molasses Acts 1773 ruined his lucrative West Indian trade.
Isaac Sears was part of the more radical Patriot Faction itching for a war with Britain.
George Washington represented a more moderate faction, willing to go to war, but also willing to wait for the Continental Congress to make a clear declaration authorizing hostile actions. To Washington's perspective that had not happened yet by July 1775 and would not happen until the Declaration of Independence July 4, 1776.