The savings rate still applies; it determines how fast you can pay off the debt. If you can reduce your spending and increase your savings rate, you'll pay off the debt that much faster, and the same principle applies once you've paid it off and started investing.
I'd caution that you should still keep a small cash reserve for emergencies, of course. Savings are liquid: student loans are not.
The general advice I got was that if the loan interest rate is less than 6%, you're better off investing the majority of your excess cash into something like an index fund since it theoretically will give you >6% gains.
However, I hate the stress, mental overhead, and risk involved in owing somebody money, so I decided to automatically save 10% of each paycheck (set up direct deposit to funnel 10% to a separate savings/investment account) and essentially contribute as much as possible after that to student loans.
I'm happy where I currently am - almost out of debt and with a non-trivial amount saved up. The key for me was automatically moving the first 10% to savings then setting an ambitious goal each month to put toward debt. Good luck!
I'm not one for biblical citations, but "the borrower is slave to the lender" always gets to me.
Burning question: what to do when you have (education) debt? Do you put every spare dollar in repaying it or still inculcate a habit of saving 20%?