As far as I can tell, what you need to be doing is remembering X and Y between each loop cycle, like johnwasser was suggesting.
Basically, you'll just need to be adding or subtracting your value from some remembered value that then gets written to each servo each time.
#code
//Not actually code, I'm making up functions and such below
int servoX = 90;
int servoY = 90;
loop(){
servoX += readJoystickX(); //This could be a negative to indicate negative axis motion
Servo.write(servoX);
servoY += readJoystickY(); //Same as above
Servo.write(servoY);
}
#/code