Problem with SIM800L GSM module and servo
You SIM800 module will pull 2Amps when its transmitting.  If your servo is also trying to overcome the inertia at the start of a movement it will pull 4+ times its normal running current.

A 9 volt battery will let you pull a couple of hundred milliamps.  So when the GSM transmits you system will shutdown.

You need a proper power supply or a battery pack that can put out these levels of peak current (3+Amps)