If you are using Alfresco 4, Share has a Tag Management Console. You'll find it under More, Application, Tag Manager. For a given tag there is a set of actions in the right-hand side of the table, including Delete.
If you are using Alfresco 3.4, you might be able to get a handle to the tag by using its node reference and then delete it using JavaScript or Java. You can find a tag's node reference by browsing to the tag in the Node Browser. For example, a tag called "test1" would reside in: /cm:categoryRoot/cm:taggable/cm:test1
If this is production I would highly recommend testing this before trying it.