Yes, you may use a REST call to delete. See DELETE for the "saved/searches/{name}" endpoint.
https://docs.splunk.com/Documentation/Splunk/6.5.1612/RESTREF/RESTsearch#saved.2Fsearches.2F.7Bname.7D
Please keep in mind that the Splunk Search interface command line provides a 'rest' command, but this is read only, and is not a true REST client. Please use your favorite common purpose REST client. (curl, Postman, any HTTP library)
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