To clear up console storage you can remove Content Files like Special Ops Pack or Multiplayer Pack and re-download them whenever you want.
Call of Duty Modern Warfare can consume a lot of storage space, you can remove the content files safely to free up hard drive. You can do this on your console and remove COD Modern Warfare Content files that you are no longer wish to use. Here is a guide on how to safely delete Modern Warfare Content files to free up storage space. Do not worry there will not be any game crash issue.
By deleting COD Modern Warfare content files mean managing the DLC Pack installations. This content can be re-downloaded anytime but if you are not using it you can remove them and free up your console storage.
Ignore Data Pack 1 and you can remove anything and select Uninstall to remove that content files completely. On PlayStation press X to uninstall, below is the list of things you will find under the Game Installs and details of each content type.
Data Pack 1 is responsible for the Campaign, Multiplayer, Spec ops, so avoid removing this one. But you can get rid of others like Multiplayer Pack of Special Ops if you are not accessing those content in the game. This will clear the content files and clear up storage space.
Just in case you remove something by mistake or want to back visit the store and re-download it. All content will remain active in your account. This is useful when you have low space left and unsure of what to remove. At that point, if you have COD Modern Warfare then you get rid of Content Files for a while.