The answer is probably yes, but it depends upon what exactly the "Smart Card" is. Simple cards are no more complex than I2C Eeprom in a flat-pack. Those which are PICmicro/AVR + I2C Eeprom will either need programming with a suitable interface between PICAXE and embedded Eeprom or any pre-programmed protocol would need to be implemented. Smarter cards have a simple low-level interface but a more complex higher level protocol and a 'file system' of sorts.
Well, you should be able to read and write a simple EEPROM SmartCard through I2C. I wanted to do this but I didn't find the time to play around.
There is a similar project here that read smartcards <A href='http://www.serasidis.gr/circuits/telecard_reader/telecardreader.htm' Target=_Blank>External Web Link</a>. Maybe that will give you some hints.