Can i use micro-USB cable to power up Milli board and Arduino ?
No. You Can't. Use micro USB to power up Arduino board and 3-pin UART cable for Milli.
Is there any other option to power up Arduino without computer or laptop ?
You can use AC-to-DC adapter or battery. For this, you need to use 2.1mm barrel standard power plug with an allowed range of 5-20 volts.