Born in Kirkwall, Orkney, Cursiter studied at Edinburgh College of Art. Following the 1912 Futurist Exhibition in London he was inspired to paint a series of oils and watercolours based on Futurist conceptions.
Cursiter served on the Western Front during the First World War. In 1920 he spent six months at Cassis and Avignon, painting both the landscape and architecture of southern France. These were mostly executed in an accomplished and fluent watercolour technique, their vibrant colours demonstrating a marked affinity with the Colourists. During this period he was also noted for his elegant oil portraits and studies of girls in interiors.
Cursiter's Orkney paintings were produced over a fifty year period but, unlike his other work, show a consistency of style and treatment that hardly changed at all. He shares with Cadell a fascination with a particular coastline and horizon.