In our experience, the tax appraiser's office will use market value (using comparable sales) and not purchase price.
Make sure you run comps, but if you are getting a great deal, it should make up for the tax issue.
The house you purchase will be reassessed when you purchase, but not necessarily based on your purchase price, the county assessors office will assess according to "market value". As a home owner you have every right to dispute the tax assessment of your property and can even hire companies that will do it for you.
Take a look at this article I wrote as well http://agentgenius.com/?p=895
We've sold a couple of properties in the shores for less than the tax assessments and that's exactly what the new home owners are doing. Your Realtor should be able to guide you as to the "market value" and to companies that can help you with the dispute.
It doesn't matter whether the former owner had Homestead exemption or not.. YOU cannot adopt his exemption, and your purchase will be at today's assessment regardless, without exemption. So yes, it is likely that, depending on the county's assessment, you will be paying at least 2% of market value (depending on Miami Shores' city millage rate also).
Are you selling a home in Florida to purchase this one? If so, you may be eligible for portability. Call me as soon as possible so I can check this all out for you.