How does fed cutting federal fund rate affect student loan If fed cuts rate, it means it's cutting federal fund rate right? then why do loans like credit card and stuend loan? those aren't like Mortgage rate which the fed cuts its rate by buying MBS
The Fed funds rate is the rate at which commercial banks can borrow reserves on the overnight market (see this explanation at Investopedia). As such it affects all other interest rates banks charge since when they can borrow more cheaply they can also lend money cheaply to  consumers.
This affects among others also student loans (when they are provided by commercial banks - some places have government provided and subsidized $0\%$ interest student loans). However, of course if you already had a loan in a past it will only be affected if you took it at variable interest rate or if you are taking out a new loan, the fixed interest rate loans won't be changed retroactively.