I am starting a clothing business and have a manufacturer in Mumbai, India. Do I pay and Indian tax and/or a US tax for importing/exporting?
As far as India export taxes are concerned you can take a look at the Export procedure taxation website to get some idea but unless you are planning to do this yourself I would either contract with a shipper that would handle the procedures for you. Or have the manufacturer bake in the export taxes (if any) directly into the cost of the garments they ship you.
I would also contract with a customs clearing agents here in the US like Cleared and Delivered (used as an example only) to handle your customs clearance and delivery to distribution site.