You can't use iCloud to store data that you want to be able to access without having it on your phone. You will still have a copy of the data on your phone so you can access it with you aren't connected to the internet. And if you delete any synced data from your phone, it is also deleted from iCloud. In other words, iCloud is designed to sync your data across your devices, stream photos between your devices, and back up your devices. It can't be used to increase the capacity of your devices by offloading data to iCloud, and purchasing additional storage in iCloud doesn't give you more storage on your phone.
The only exception to this is if you subscribe to iTunes Match. If you do, you can access your iTunes music library (subject to some restrictions) from iCloud without having to store it all on your phone. But even here, when you play your music, it still downloads to your phone in the background.
If you need to free up space on your phone you'll have to delete or sync some of your existing data off it in order to free up space.