It comes after Ruskin College's governing body agreed to cut two of its six BA programmes and one of its three MA courses to save money.
College principal Chris Wilkes said the decision was related to "low student numbers rather than any other reason".
He said it would continue to focus on adult education.
Famous Ruskin College alumni include former deputy prime minister John Prescott and Dennis Skinner, MP for Bolsover in Derbyshire.
BA English Studies, BA History with Social Sciences and MA Women's Studies are being discontinued.
Anne Hughes, 63, from Thame in Oxfordshire, has been studying BA English Studies part-time at the college for two years.
She said she was "absolutely distraught" it was being cut.
She is physically disabled and has depression, and said she chose to study at the college because it worked with "disadvantaged, disabled and mature students".
The college also offers bespoke timetables, unlike some other places of higher education, she added.
Online petitions have been set up in a bid to save the English faculty and the Women's Studies course.
One signatory, Jenny Lewis, wrote on the first petition: "[Tutors] Helen Kidd and Tom Sherry are carrying on the great Ruskin tradition of bringing opportunities to those that otherwise would not have them."
Student and activist Saskia Ritchie, who set up the second petition, said Ruskin had been set up for "people who would traditionally be excluded from academia" and gives "access to truly excellent learning opportunities".
Mr Wilkes said the college would lose about 25 students as a result of the cuts.
He added degrees had been on offer at the college for about 10 years and were "relatively new" considering the college's 116-year history.
"Our focus will continue to be on educating adults and I think what we're doing is just renewing our offer but doing it in a different way, fulfilling our mission in a different way, to perhaps how we've done it in the past," Mr Wilkes added.
The college previously lost funding from the Skills Development Agency.
An Oxford college has moved away from its founding principles of providing degrees for working-class adults and mature students, students have warned.