You can build a clone of just about any website using WordPress. The question, though, is how much work are you willing to put into it? Since you're already asking for tips/tricks and plug-ins, I'm guessing you want to make a quick clone that requires little to no additional development time.
That said, here are the basic features of Groupon that you'll need to reproduce:
Different listings for different regions/cities
You can do this several different ways, but the easiest would be with a custom taxonomy for your site. Each city or region would be a taxonomy term, which you can use to separate and categorize the posted deals.
Displaying deals for different regions would require you only to add a region-specific filter to your query.
The core of Groupon is the ability to actually purchase the posted coupons. You could set this up with just about any of the e-commerce or shopping cart plug-ins available in the repository.
Every Groupon deal expires after a certain period of time. You can achieve the same kind of functionality with the Post Expirator plug-in.
There's no real value in Groupon if people can't share it with others. I'd recommend a Facebook Like button or a Tweet This widget somewhere so people can broadcast deals as they're found.