Unlink iphone contacts

hello,

Remove the account where they are linked to. For example:

If your contacts are linked to gmail, hotmail, yahoo and so on, go to settings>> scroll down and tap Passwords & Accounts

select your mail address and delete it or switch off contacts option

that way you can remove them from your device

If they are linked to iCloud do the steps below:

Go to settings>> [yourname]>> iCloud>> switch off contacts option

Note: if contacts are located into iCloud and you turn off contacts they won't be deleted from your account but your iPhone

see more here:

https://support.apple.com/kb/PH2664

Regards.