I wrapped up a 7 year stint in grad school (masters, then PhD at a different school, both in environmental science) almost exactly one year ago, so I figure I'm still allowed to chime in with my perspective.
In terms of earned income lost, grad school (especially the PhD) is terrible, but it is a great opportunity to grow your frugality muscles. You have a lot more freedom in how you spend your time, which helps a lot in getting started. After grad school, I moved into industry and make 3-4x my student stipend, but by continuing to practice the same frugal habits I developed in grad school, my savings rate has really accelerated!
I graduated at age 30, having worked for 1 year before starting grad school, earning what was essentially a grad student wage ($25k/year, whoo!). My stipend ranged from $20k-35k/year (I had a fancy ass fellowship for 3 years which was 30k, one bumper year with fellowship+some extras, then the remaining years at a more normal stipend of $20k). When I graduated, I had a net worth a little over $50k, and I had also paid off about $12k in student loans. I didn't closely track my savings rate for much of my time in grad school, so I'm not sure exactly how much of that is actual savings vs. investment growth (though I started seriously investing money right *before* the 2008 crash. Oh yeah, and the PhD part of grad school was done in a rather pricey part of California--my rent was betweeng $750-850/month for 5 years, and that was considered really bargain rate.
Some stuff I was lucky with: I went to a really cheap undergrad college and got out with minimal debt. Also, my parents sold me their old car for $2k, which spared me the hassle of a dealership and the sinkhole of a car loan (though I'm still not 100% certain this was really "luck" as I then had to insure and maintain the thing!).
Things I was actively careful about: Always going for the cheapest housing I could find (as long as the area was not totally crime-ridden and was within biking distance of school/groceries, I was not picky about location/ambience--this will save you a TON of money and it only requires the upfront investment of time to look for a good place), limiting going out (try to organize cheaper social activities like potlucks instead), use the library for entertainment, bike/walk/bus everywhere, and pretty much never going to the mall or otherwise engaging in recreational retail activities. Camping weekends instead of going somewhere that would require a hotel. Generally evaluating whether or not something was really going to add value to my life before plopping down money for it.
As far as whether or not you should be trying to save aggressively, my advice is to treat it like a job, don't count on having a fancier better job later. Sure, you probably aren't going to save 75% of your income, but do as much as you can and at least try to max out the IRA. Some people will make 3-4x their stipends right after grad school, a lot of people will wind up as postdocs or adjunct professors earning $40k/yr for a while. Of the ~10 people who graduated in my cohort, I think only 2 are making 6 figures, most are earning in the $40-50k/yr range, and then a few others are in between those two ends. I have another friend who just finished and as of yet has NO job lined up, which is not as uncommon as you might think (another friend did a PhD and 2 postdocs and has now been seriously underemployed for several years).
I'm not saying people should be totally depriving themselves, but just think critically about your spending and whether or not you are really getting anything out of where your money is going. I had so many friends who did things like buy coffee on campus daily, or go out to dinner once or twice a week just because. Or who just HAD to live downtown, even though it was more expensive (and even though you could easily drive or take the bus there on the weekends, if you needed your going out fix). These friends wound up with credit card debt or student loans or debts to the bank of Mom and Dad. No fun.