Can you post an annotated schematic showing exactly how you have wired it. Be sure to include all connections, power, ground, and power sources. Also post links to technical information on the hardware items.
It is working the way it was designed to do. Note: you are probably going to destroy your UNO in the process. Go back and redesign your system. Here is some information from your link. You need to also consider the other loads in the system and the locked rotor current of your stepper.
Specifications:
Voltage: 12VDC
Operating Current: 1.7A per phase [your adapter is rated at 1.5]
Stepper Control: 4 wire
Torque: 54g/cm2
Holding: Torque 40g/cm2
You will not get that to work properly. You will have two phases on at one time that is 3.4 amps. The driver is rated at 4A max, it will run extremely hot unless properly heatsinked. The cycling this will cause your power supply to do will throw a lot of nasty spikes into the power supply, probably destroying your Arduino and possibly the port on your computer.
Nooo.
Look at the datasheet. This is a 1.5ohm stepper.
The 8volt that the L298 outputs on a 12volt supply will draw 8/1.5 *1.4 = 16.8Amp.
That will fry the supply or the driver or the stepper motor.
The L298 is totally wrong for this motor.
This stepper needs a current controlled stepper driver, like the DRV8825.
With the current properly adjusted to about 1.5Amp.
Then the 12volt/2A supply will be fine.
Leo..