He was born in Perth, Victoria County, New Brunswick, the son of Benjamin Beveridge and Joanna Taylor, and was educated at Mount Allison College. He worked in his father's store, later taking over the business, and also entered the lumber trade with his brother Henry Douglas. In 1862, he married Jane Elizabeth Stevens. Beveridge was postmaster at Andover, also serving as justice of the peace and as major in the local militia. In 1867, he ran unsuccessfully for a seat in the House of Commons. He was a member of the Masonic lodge. In 1882, he was named to the Legislative Council.
