Can a TRUNCATE or DROP table ever be very time consuming?
MyISAM -- DROP is like a file delete.  TRUNCATE performs the C file action of removing all the data but leaving the file in existence.
InnoDB with its own tablespace (cf innodb_file_per_table) -- like a file delete
InnoDB without its own tablespace -- lots of blocks to free up; this could take time.


A file drop can be fast or not so fast, depending on the Operating system.  Some OS's run around freeing up the blocks right then and there; you have to wait.  And, because it is an OS operation, this may interfere with virtually anything else.  What OS?

"Minutes" seems long.  How many minutes?  How many GB?