Baxter started his career as a journalist at Capital Radio in 1989. He later worked as a Producer at BBC Radio 5 Live, the BBC factual television programme Top Gear, and at Independent Television News (ITN). In 2011, he directed his debut feature documentary, You've Been Trumped, which won best environmental film award at the Sedona Film Festival, won the Maysles Brothers Award at the Denver Film Festival and won the Sheffield Green Award at Sheffield DocFest. In 2014, he directed A Dangerous Game, which was nominated for the audience award at the Edinburgh International Film Festival and the Sheffield Green Award at Sheffield DocFest. He directed the sequel to You've Been Trumped, entitled You've Been Trumped Too, released in 2016.
Baxter's 2021 documentary Eye of the Storm, premiered at the Glasgow Film Festival, prior to its broadcast on BBC Two and won the best specialist factual at BAFTA Scotland.