You have a source local (or remote) folder, where new files are being added by some external process. You want to make sure that these files gets regularly transferred to remote (or local) folder. And you want to remove the source local (or remote) files once they are safely transferred.

First of all, such an operation should not be called synchronization, as it does not end with source and destination folders being synchronized. Anyway, leaving a terminology aside…

Supposing you never end with the same file being both in source and destination folder, you can simply move the files to the destination folder.

You can do this using -delete switch of the put (or get) command. WinSCP deletes the source file, when it is successfully transferred to the destination folder only.

If it can happen that the same file is both in source and destination folder, you can use synchronization and delete only transferred files afterward.

Perform the synchronization using synchronize command. Make sure the script generates XML log file. You can then parse the log file to enumerate files that got successfully transferred, and use the list, to generate script to delete the source copies.