Graber was raised in Wildwood, New Jersey where she still owns a home. She studied under poet Stephen Dunn and went on to earn her BA in philosophy from New York University. She quit teaching middle school English to afford herself the ability to enroll in an MFA program and pursue a career in poetry. Kathleen said of the experience, "Most poets live humble lives, I think, and maybe that is by temperament or design, or maybe it is just a necessity."
Graber has earned many awards for her work including the Rona Jaffe Award, the Amy Lowell Traveling award, a National Endowment for the Arts award and the Guggenheim award. She is a Hodder Fellow of Princeton University, a National Book Award finalist and a National Book Critics Circle finalist.