Dumping a log file while reading from it?

Im working on a project (using a FEZ Panda Tinkerer kit) where I log NMEA sentences to a SD card. The logging is set to one record every 5 seconds. That part works fine but Ill also want to be able to dump the complete log over Xbee without having to stop the logging.
PS. the log file can be rater large so it will take several minutes to complete a dump.
What is the best way to handle this?