The field issueLinkType does not support the operator IS, which makes it impossible to write a JQL query to exclude a specific issue link type from its results. That occurs because issues without links will also be matched, and there's no way to specify a null value for issueLinkType.
For example, when running the JQL query below:
All issues having an issueLinkType different than blocks will be returned, including issues without any links.
Implement support for the operator IS on the field issueLinkType. That would allow the JQL query above to be rewritten as:
Which would return all issues in project SCRUM, having issuetype Story, having at least one issue link type different than blocks, and having a status different than Done.
One can create a special saved filter containing all currently available issue link types and use nested filters.
The downside is that any modifications to issue link types, such as adding a new one, or renaming/deleting existing ones, would break this functionality until the filter is updated.
Then in the final JQL: