This find oneliner displays all the broken links in the current directory. By adding xargs rm, you can delete all the broken links found.
Find all the broken links:
$ find . -type l -exec sh -c "file -b {} | grep -q ^broken" \; -print
Delete all the broken links:
$ find . -type l -exec sh -c "file -b {} | grep -q ^broken" \; -print | xargs rm