There is a Delete button in the Beginning Balances Journal for Projects, but it is not functional. (Technically, it is functional but only if you remove every single line from the Journal 1 by 1.) But...even though there is a select all option, when you select more than 2 lines the Remove lines button is greyed out. So if you have a journal with 1,000's of lines, you'd have to remove each line 1 by 1. And then (and only then) you can use the delete button.
I filed a support ticket and the response is that it is not a bug because it didn't work in the former version of AX / Operations either. LOL. Please help us delete journals that we want don't want to post.