Firstly go to this person's profile and at the very very bottom of their page just click Remove from friends.
This person never knows when existing friends had already removed from their Facebook friends list.
The numbers that represent your total friends will decrease but Facebook won’t reveal the name of the person who just removes you.
To be sure that this person is not being able to see your profile anymore put this person on your blocked list.
Click Settings on the main menu and select Privacy Settings, find the Block List and type the name on the Person text box and click Block to match the name. After you confirm the name, in the Block List will appear the person's name.
You can remove this block if you change your mind later on; it's really not a permanent blocking.
With this action the person won't be able to see any of our activities on Facebook just like you deleted your account to this person. Hope this tips can help.