Your avrdude command and options should look somthing like...
avrdude -p atmega2560 -c stk500v2 -P COM10 -b 115200 -U flash:r:flash_backup_file.hex
-c stk500v2 is how the bootloader in MEGA2560 talks
-P is the serial port, that may be the address thing you were seeing (not sure) but you need to know which port
-b 115200 is the baud rate (not sure if it is 57600 or 115200, it should not hurt to try both)
-U flash:r:flash_backup_file.hex is the key to reading ... notice the r ... where the :r: is ... that is for reading.
to backup the eeprom (a good idea)
avrdude -p atmega2560 -c stk500v2 -P COM10 -b 115200 -U eeprom:r:eeprom_backup_file.hex
if you want to write it back to the board
avrdude -p atmega2560 -c stk500v2 -P COM10 -b 115200 -e -U flash:w:flash_backup_file.hex
-e will nuke everything which you probably need to do befor writing.
avrdude -p atmega2560 -c stk500v2 -P COM10 -b 115200 -U eeprom:w:eeprom_backup_file.hex
an explicite erase is not needed with eeprom.