As a young man, Wyman moved to Keene, New Hampshire, and served in the New Hampshire Provincial Regiment during the French and Indian War at the Battle of Fort William Henry and the Battle of Carillon in 1757 and 1758 respectively.

Wyman was chosen to represent Keene at the New Hampshire General Assembly in January and February 1775.

At the outbreak of the American Revolutionary War in April 1775 Wyman, as a captain of the local militia, led a company from Keene to the Siege of Boston and joined John Stark's 1st New Hampshire Regiment in the Battle of Bunker Hill.

In 1776 he was appointed as colonel of a New Hampshire militia regiment sent to reinforce the Continental Army in its retreat from Canada.

He would go on to become a justice of the peace in his home town of Keene, New Hampshire, until his death on March 31, 1792.