Watt was originally known for her figural work. However, in her 1997 exhibition, Fold, at the Fruitmarket Gallery in Edinburgh, she introduced expertly rendered fabrics into her work. In 2000, Watt expanded her work with fabric in her show, Shift, at the Scottish National Gallery of Modern Art. She was at the time the youngest female artist to ever show there.
Watt was awarded the ACE Prize for her painting, Still, in 2004. In 2005, Watt attended the Glenfiddich residency. She then became Associate Artist at the National Gallery in London in 2006. Her time there was spent further exploring fabric, especially in the painting St. Francis in Meditation by Juan de Zurbarán (Spanish, 1620–1649). In 2008, Watt exhibited Phantom, a set of paintings she made while at the National Gallery.
Watt currently lives and works in Edinburgh. She is represented by Ingleby Gallery, and has works in collections such as the Uffizi and the National Portrait Gallery in London.