The Sitecore page
PublishQueueStats is used to see the stats of the Publish Queue on the master, web, core and filesystem. Normally, we focus mainly on the master database as it is there that content changes and needs to be published from.
Even if you clear the Publish Queue table on the master database, it will not affect the job queue of the Publishing Service. The publish queue table is mainly used by the incremental publish to see what items need to be published.
For your case, the workaround, if no "Sitecore" way is available, is to directly go to the SQL and clears the Publishing_JobQueue.
After some analysis on the Sitecore Publishing Service assemblies, I can say that the delete functionality has not been implemented as of now (version Sitecore Publishing Service Module 9.3.0).
From the namespace
Sitecore.Publishing.Service.Data with class
PublishingJobProvider, we can see that the
Delete method has no implementation. Please see screenshot below