How to run hair trimmer's motor normally (without pulsing) using 12V/1A charger? Its orignal cell battery uses 1.34V and 0.34A
You have already discovered that speed is proportional to voltage. Current is proportional to load torque when the speed is stable. However the current require to start the motor is higher than the current required for steady speed. Attempting to start the motor with too much voltage is apparently causing your charger to shut down. As soon as it shuts down, the current ceases, so the charger recovers and tries again.

DC motors work best when connected to an electronic speed controller that limits the current. With the current limited to the proper level, the motor doesn't try to get up to speed quite as quickly.

For a small motor that doesn't need speed adjustment, you can use a power supply that can either supply as much current as the motor requires to start or limits the current somewhat by internal resistance and is not harmed in the process. Small batteries can power small motors that way.

Try the lowest voltage power supply that you can find. You can probably find a 3-volt supply. You can limit the speed by putting a resistor in series with the motor. If you use one to three diodes in series with 3 to 5 volts to limit the voltage, the motor speed will be somewhat less effected by load variation. That may also be easier than figuring out the resistor value.

Based on information in a comment that should be added to the question:


  on its orignal cell battery it uses 1.34 v and 0.34 Amps.


To reduce the voltage of a 3 V supply you need to drop to 1.34 V. That means 3 - 1.34 V = 1.66 V across a series resistor with 0.34 A or 1.66/0.34 = 4.8 ohms.