For sure it’s not possible to do it manually, but there is currently no all in one web-service to do this easily.
So you will probably have to rely on a script and on api/issues/search as well to retrieve all issues of that specific user. Then you can feed those issues to api/issues/bulk_change with the empty
assign parameter to un-assign them all.
And you will probably have to call both those web-services multiple time because the one to search issues is paginated to a maximum of 500 issues per requests and I think the one to do bulk change accept a maximum of 250 issues per call.