Will the Radeon 7770 work with my Asus P5VD2-MX SE?

The motherboard does have a PCIe x16 slot Yes, it is compatible with your motherboard...

There are other things you must also check like if the CPU will not be bottlenecking your GPU or if your PSU can handle the 7770, but if the question is compatibility, yes. it is compatible.

As said above PCI-E x16 is available so the card should be compatible. But, I can't say it is 'compatible' yet before I see the CPU (if there is bottlenecking), PSU and the space on the case.