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.
Coupon Purchase
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.
Deal Timeout
Every Groupon deal expires after a certain period of time. You can achieve the same kind of functionality with the Post Expirator plug-in.
Social Networking
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.