Mullen started out performing mostly episodic and background characters on The Muppet Show (most notably Gaffer the cat), as well as assisting on the feature films.
She advanced to a lead puppeteer on The Dark Crystal (operating the heroine Kira) and was one of the core regulars on Fraggle Rock, as Mokey Fraggle and Cotterpin Doozer, among others. She continued to work with the Muppets on a more sporadic basis in the late 80s and 1990s, notably on The Wubbulous World of Dr. Seuss (as a first season regular, notably playing Morton the Elephant Bird, and as a second season director).
One of the creators and performers of Between the Lions, other non-Muppet credits included assisting Frank Oz with Yoda in The Empire Strikes Back and the series Allegra's Window. In 2004, Mullen and husband Michael Frith worked with No Strings International to create and perform an educational puppet show for children in Afghanistan.