This is interesting but I'd say you're in the minority compared to most businesses that try Groupon (like restaurants, cafes) and have high fixed costs and slim margins.
Restaurants pay about 40% for food. The rest is payroll, rent, etc. In total, they make about 4%, but they lose money hand over fist if the restaurant is empty.
Also, that margin is very rubbery, depending on the dish. They might make a pasta dish for 20% of the cost, and a steak for 70% of the cost.
Also, drinks can have crazy mark-ups.
If the groupon is limited to high-margin meals, then they won't lose money. And they might make a profit on the drinks, or people who change their mind and go for a full price dish.
And they might get some repeat business. Also, it looks good for them to look full - passers-by might assume that the restaurant is packed because it's a good one.
The thing is, owners have to be very careful about the deal they give. Groupon seems a little unpredictable (for non-experts), so it can be very dangerous.
Of course, all marketing has its costs. And restaurants and cafes rarely rely on marketing (fast food excepted).
here you go :)