Removing the data from the mp_IndexingQueue isn't going to help you much.
Notice most of the space is being used by your log which suggests the database hasn't been properly backed up for quite a while. See how the total for all of the tables you listed doesn't add up to anything close to 3,956 MB total usage you listed? Your regular database size is 218MB which isn't too outrageous if the site is rather large.
If regular backups are occurring, the problem is probably just "leftover" from when it wasn't being backed up properly. Basically, in the SQL Server world shrinking databases is seen as taboo because, among other things, it reduces the performance of a database if it must grow on disk to accommodate the data it needs to store. Usually I would be in line with the argument but when a database has unnecessarily grown to a size it would not naturally be due to a misconfiguration of the server, database, application, it is absolutely necessary.
Here are some good articles on this subject: