Yes. Rules can be created to automatically add or delete tags from a contact. This can be accomplished using Tagging Rules in Nurture.
Go to Settings tab by clicking on the gear icon located on the top right corner.
On the left pane, click on Tagging Rules. Here you can define a rule for adding a tag to contacts based on activity performed, attributes, form fill, etc. Select the appropriate rule. Select the tag to be added or removed. Click on Add. Within a few minutes, the selected tag will be added / removed from all the contacts satisfying the defined rule.