Are you using OWA?  The outbox is not seen in OWA, you must open the outlook client to view the outbox.
If you want to view the outbox in OWA you can follow the instructions in the below link to add it to your favorites in OWA
ref link:  https://answers.microsoft.com/en-us/outlook_com/forum/all/outlook-outbox-missing-in-office365/538e111c-40d6-47ac-941b-125c3f038abe

Fox:  What is "OWA"?  

Lee:  I found the Outbox, and there was something there.  It was from some time ago, and I didn't need it, so I tried to delete it but it wouldn't delete.

Phil,
OWA is outlook web access.  Nevertheless I'm glad you have sorted it out.
If you want to delete what is in the outbox drag it to drafts and then delete it from there.

Try moving it to another folder and then deleting it.  

I've seen things get stuck there before.  If you still have issues getting it to be deleted and this is connected to an Office365 account, another way might be to turn off the caching (temporarily).  Go to File tab, Click the Account Settings button, then Account Settings in the list.

In the window that appears, click on the account and then click change.

And then uncheck the Use Cached Exchange... box and next until you can close.  Restart outlook.  Then go back and re-check the box.  That should rebuild the local copy of your mail and since the stuck message was likely in that old local copy, it should be gone.  NOTE: rebuilding the cache may result in Outlook appearing slow for a time and/or losing search effectiveness for a while as it rebuilds it's indexes.

Thank you.

Won't you just find it in you Drafts Folder on either OWA or your local Outlook client.