If you are calling Day One from Drafts with a simple URL call…
Drafts can set custom tags - kind of like a variable. See setTemplateTag().
You could assign the content of the draft to that tag and pass that instead of the draft content as the parameter to Day One. This would allow you to also clear the ontent of the draft before calling out to Day One.
e.g. as a script step
draft.setTemplateTag("fordayone", draft.content);
draft.content = "";
draft.update();
If you are calling Day One from Drafts with an x-callback URL call…
Once you are returned to Drafts, if you have set the option to wait for a response, the Draft will continue execution of the action. Adding an action step after the x-callback to clear the content of the draft would be a simple addition.
As a script step in the action:
draft.content = "";
draft.update();
Hope that helps.