Testa was born in Philadelphia and has one sister. At age four, her family moved to Rhode Island. She studied acting at the University of Rhode Island. Testa left school to move to New York in 1976 to pursue a performing career.

Testa made her film debut in Going in Style (1979), and has appeared in numerous movie and television roles since, including Sophia in the 2003 sitcom Whoopi, Zia Maria Luisa in the 2014 film Big Stone Gap, and Sister Clare in the 2004 film adaptation of Tony n' Tina's Wedding. She also appeared in such films as The Business of Strangers (2001), Stay (2005), Eat Pray Love (2010), The Bounty Hunter (2010) and the TV series Law & Order, 2 Broke Girls, Smash, White Collar, Cosby, Sex and the City, and Life on Mars.

Her Broadway roles include Joyce Heth in Barnum (1982), movie columnist Hedda Hopper in Marilyn: An American Fable (1983), Angel in The Rink (1984), Domina in A Funny Thing Happened on the Way to the Forum (1996–1997), Madame Dilly in On the Town (1998), Magdalena in Marie Christine, Maggie Jones in 42nd Street (2001–2002), the Matron in Chicago (2005), Melpomene in Xanadu (2007–2008), General Matilda B. Cartwright in Guys and Dolls (2009) and Madame Morrible in Wicked (2014).

From 1999 to 2002 she appeared frequently as the voice of Shirley the Medium on Courage the Cowardly Dog.

In addition to her show albums, Testa and Michael Starobin released an album, Have Faith, in 2014. It contains contemporary interpretations of songs by artists such as Alanis Morissette, Prince, The Beach Boys, Leonard Cohen, Finn and LaChiusa.