You just need to push an ’empty’ reference to the remote tag name:
git push origin :tagname
Or, more expressively, use the --delete option (or -d if your git version is older than 1.8.0):
git push --delete origin tagname
Note that git has tag namespace and branch namespace so you may use the same name for a branch and for a tag. If you want to make sure that you cannot accidentally remove the branch instead of the tag, you can specify full ref which will never delete a branch:
git push origin :refs/tags/tagname
If you also need to delete the local tag, use:
git tag --delete tagname
Background
Pushing a branch, tag, or other ref to a remote repository involves specifying «which repo, what source, what destination?»
git push remote-repo source-ref:destination-ref
A real world example where you push your master branch to the origin’s master branch is:
git push origin refs/heads/master:refs/heads/master
Which because of default paths, can be shortened to:
git push origin master:master
Tags work the same way:
git push origin refs/tags/release-1.0:refs/tags/release-1.0
Which can also be shortened to:
git push origin release-1.0:release-1.0
By omitting the source ref (the part before the colon), you push ‘nothing’ to the destination, deleting the ref on the remote end.