>I have three full text catalogs defined in Storage\Full Text Catalogs. When I do my import, it takes care of creating that. However, at the beginning of the import, I need to clean that out. What approach can I use to remove everything under that without even knowing the name of the catalogs and no matter if there is one or many?

Not tested suggestion. You can use sys.fulltext_indexes catalog view to get the list of indexes and drop them. After that you can drop catalogs using list from sys.fulltext_catalogs