I plan on connecting a 12V battery that gives 2 amps directly to one of these drivers https://www.pololu.com/product/2879/. Although, it says that the “Maximum current per phase […is…] 1.5 A”. Will connecting this 12V, 2A power supply directly to this driver (with this stepper motor https://www.pololu.com/product/1204), ruin the driver? Thank you.
It sounds like you are confused about how current works. Your power supply does not “push” current through the driver; the driver will only use the current it requires from the supply. The current rating listed on a power supply is typically the maximum it is capable of sourcing. Please note, you should set the current limit on your STSPIN820 stepper motor driver carrier to no more that the 600mA per phase ratting of your stepper motor; you can see more about setting the current limit in the “Current limiting” section of the STSPIN820 product page.