I used the JIRA search to search issues which have a certain entry in a "Query issue multi linker custom field":
issuetype=MyIssueType and "My Custom Query Field" = ReferencedIssue
This works.
I tried the following to list all issues which do not have the entry:
issuetype=MyIssueType and not "My Custom Query Field" = ReferencedIssue
This does not work. Furthermore, the operators "~" and "!~" (CONTAINS and NOT CONTAINS) are not supported by the issue type.