You'll need to do some googling, I can't teach a full econ class here. But the TL;DR version is that every country that tried austerity has recovered more slowly than every country that didn't. That and the entire justification for austerity was in that one spreadsheet that turned out to have a glaring error.
While true, you have to remember that the creditors were demanding austerity. Basically the creditors were telling Greece that the only way that they'd lend any more money is if Greece cut back its profligate spending.
If you switch to say, the US, creditors know that the US has far greater assets and far more people are interested in investing in the US that creditors don't have as much economic power.
You are correct in that austerity generally screws over the economy - see the Great Depression, and the intense spending and printing money that the US Treasury did helped pull the US economy out far faster. (And thankfully, the right part was in power to do so). However, that's because the US has the ability to borrow money REALLY cheaply because so many creditors want to invest in the US. The US also has a far better credit rating so creditors know they have a good chance of getting their money back.
Greece is different. People aren't so willing to invest. Pretty much all the institutional investors aren't giving Greece money. So the only reason Greece is getting any money is because the EU is being forced to prop them up, with little to no expectation of getting repaid. And they're demanding the government cut back because the government is spending more money than the economic activity they can generate.
In a more microeconomic sense, it's like spending more money than you earn. You'll eat through your savings, and many creditors will lend you cheap money at first. But continue on and if they see your debt approach your assets, they'll stop lending to you. You can still borrow, but now you're in the predatory lender category where you're basically renting to own at hugely inflated priced. You know, where you spend $50/month to rent a $500 PC for a couple of years before you own it. And miss a payment and it's repo time and you lose all your "equity".
The US is in the former category - they're basically balancing the books and have lots of assets. Greece is in the latter. And with the chaos caused by the past few weeks, they've effectively said "screw you" and the economy is in shambles. The only sector that still has promise is tourism, and even now tourists are seeing problems. Paying for stuff electronically may or may not be successful (because there's a run on the banks, withdrawals and transfers are limited, and Greeks need cash, because it's very hard to convert a card payment to cash).