So the day before US election, Narendra Modi dropped a bomb that 500 and 1000 INR notes will be dropped from circulation. I want to know the democratic/legal processes that let him do this.
There is a law available for this. Under the Reserve Bank of India Act, 1934 (2 of 1934) sub-section(2) Central Government has a powers to take back the legal status of a particular currency. This is what above section says:
(2) On recommendation of the Central Board the 6[Central Government] may, by notification in the Gazette of India, declare that, with effect from such date as may be specified in the notification, any series of bank notes of any denomination shall cease to be legal tender 7[save at such office or agency of the Bank and to such extent as may be specified in the notification]
So Modi has used above powers to remove legal status of high value currency notes. You can read more information from official notification by RBI and official notification from Ministry Of Finance also you can see the corresponding act in below link.