I don't know how but it may be possible using AT commands to the GSM?GPRS Shield. I suggest looking at the ETSI standards GSM 07.07 & 07.05 | Enhanced Commands available on line and the module specific SIMCOM AT Commands to see if it supports MMS.
Does the Arduino Uno come with software to run the SD Card protocol? If not could the board be changed to one with an SD Card socket and software. Some of the SD Card protocol specification is available on line.