Login to the DocuSign web console as an Administrator in the sending DocuSign account, and navigate to Preferences >> Features. Enable (check) the Suppress Emails to Embedded Signers setting and Disable (uncheck) the Use Envelope Complete Email for (non-suppressed) Embedded Signers. Click the SAVE button (all the way at the bottom of the page) to save the changes.
These settings make it so that DocuSign will not send any emails to Recipients that you create via the API and specify as embedded/captive (i.e., by setting clientUserId property to indicate that they will be accessing the Envelope via your application).
Update
If you are using the New DocuSign Experience then follow the instructions here
See the Document delivery section.
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