If you are running FrostWire on Android head over to My Files section of the app and long press on the file you would like to delete. When the file is selected tap on delete icon from the toolbar.
If the file you downloaded belongs to a torrent package (did not come from YouTube, SoundCloud or Archive) please go to the Transfer list and make sure that Torrent is not within that list. If it is there, FrostWire will try to find the deleted file, will not find it and the download will start again, since the Torrent Package is still in Transfers.
(If you find it there, tap the Torrent in the transfer list and select the option "Clear Complete" to remove it from Transfers).