Beaven moved to British Columbia from Toronto, where he had been educated at Upper Canada College, because of the gold rush.

Beaven was elected to the provincial legislature in 1871, the year of union with Canada, and served in the cabinets of De Cosmos and his successor George Anthony Walkem as chief commissioner of land and works.

He was accused by the opposition of corruption and was criticised for not opening up land for settlement quickly enough as well as running up the deficit.

Beaven remained an MLA and leader of the opposition until 1894 when he lost his seat in an election after having served in the legislature for twenty-three years.

Following the 1898 election, no party had a majority and the lieutenant-governor Thomas Robert McInnes passed over the former premier John Herbert Turner and asked Beaven to form a government despite the fact that he had been out of the legislature for four years.