I would like to remove my Apple ID from an iPhone

Do you want to keep both phones, but use another Apple ID on one phone? Not delete anything, but keep both phones, but have them on different Apple IDs?

Apple ID - create a new.      

Apple ID – Create         

Family Sharing.         

Family Sharing - Set up.        

When changing to the new ID, there may be some data loss, but you can minimize it. If syncing photos with iCloud, ensure Optimization is turned off in Settings/Your Name/iCloud/Photos and/or in Photos/Preferences/iCloud. Then make sure full resolution photos are on the device/computer. When signing out of iCloud, if asked whether you want to retain data, choose yes. Messages conversations will be lost if they are addressed to the ID. See the article below for other places that the old ID should be removed. See Winston Churchill's response in the below discussion. Also set up Family Sharing between the IDs to keep access to your apps/purchases. 

How to switch Apple IDs on your iPhone or iPad.      

How to transfer all files from one iCloud account to another.        

What to do after you change your Apple ID or password - Apple Support.     

Do this to the one you want to give away:

What to do before selling or giving away your iPhone, iPad, or iPod touch. Click here --> https://support.apple.com/HT201351

You don't need to separate them, just erase the one you don't want and make sure you remove your Apple ID from it too. That's why I posted that link.