Serving with English forces in the Netherlands during the Dutch War of Independence, Axe traveled to the British colony of Providence Island, in the western Caribbean Sea, where he assisted in the construction of its central fortress in 1629. However, after a disagreement with Daniel Elfrith (possibly over the capture of Spanish and Portuguese slavers during the early 1630s ), he soon left the island with Abraham Blauvelt and Sussex Camock and sailed for Honduras in 1633.
Although briefly returning to Providence to assist the island's defense against Spanish attacks in 1636, Axe had a successful privateering career delivering a captured prize, with a cargo including gold, silver, jewels, indigo and cochineal, as he returned to England in May 1640.
Following the capture of Providence by Spain in 1641, the Providence Island Company was dissolved. Escaping to St. Kitts, Axe would later take part in a privateering expedition under Captain William Jackson to the West Indies from 1642 to 1645, in which the privateers managed to capture Jamaica.