The process of removing contact tags is fairly similar to adding a tag.
Here is how you can do it:
Find the tag you want to edit and click Browse in the last column
The page displays all the contacts that have been tagged
Click Edit Multiple and select contacts you want to un-tag
Click the blue Edit (number of contacts) button
Select the tag from Remove Tags drop-down menu
Click the blue Make Changes button
The selected contacts will be un-tagged
You can also remove multiple tags by repeating the same procedure