Then follow the standard method and delete from the table in batches in clus key order.
In order to do that, you might first have to go thru the table and store the clus key values of all the rows to be deleted. Hopefully all rows with the same clus key value are either all deleted or all kept.
Loop thru the key-values-to-be-deleted table, deleting say TOP (5000) rows each time (or however many rows work out best to delete per query). Generally I'll add a small delay after every n deletes, for example, wait 1/4 or 1/2 sec after every 50K or 100K deletes.
If the db is not in simple mode, you'll want to do very frequent log backups are you're deleting to make sure the log doesn't need to grow to log the deletes, esp. since disk space is an issue for you.
SQL DBA,SQL Server MVP(07, 08, 09) Prosecutor James Blackburn, in closing argument in the Fatal Vision murders trial: "If in the future, you should cry a tear, cry one for them [the murder victims]. If in the future, you should say a prayer, say one for them. And if in the future, you should light a candle, light one for them."