I know that arduino cant give output of 2.5A, so my question is, how should I power that motor?
It says that rated voltage is 3.1V, so, do i need some 3-5V adapter with minimum output of 2.5A?
The rated voltage is irrelevant. What matter is the current. You need a specialized stepper driver. Something using the TB6560 chip would probably be suitable for that motor. The more common DRV8825 and A4988 cannot provide enough current.
With a specialised stepper driver you can limit the current to protect the motor and use a 12v or 24v power supply.