Student Loan Relief Act of 2017 This bill amends title IV (Student Assistance) of the Higher Education Act of 1965 to cap the interest rate for new Federal Direct Stafford Loans and Federal Direct Unsubsidized Stafford Loans that are disbursement on or after July 1, 2018. Specifically, the bill caps the rates for: (1) undergraduate students at 4%, (2) graduate students at 5%, and (3) parents of undergraduates at 6%. In addition, the bill eliminates loan origination fees charged to students to process their loans. Finally, the bill establishes a program that allows eligible students with existing loans under the Federal Direct Loan program (a Federal Direct Stafford Loan, a Federal Direct Unsubsidized Stafford Loan, a Federal Direct PLUS Loan, or a Federal Direct Consolidation Loan) to refinance their loans down to the lower rates offered to new federal borrowers in the 2017-2018 school year. The program must also allow students with loans under the Federal Family Education Loans program to refinance them as federal direct loans.