Trim An Outline To Achieve A Specific Angle End Point

The attached is a logo I'm working on.
There is red filled type ("D") overlapping a stroked thick line in the attached screen shot.
I'm trying to achieve end points that have perfect vertical and horizontal cuts as shown by the white box behind the type.
However the finished logo will be using in a layout that has a color background, and the white boxes show.
Expanding appearance does not work. Compounding does not. Masking does not.
I could take the logo to Photoshop and remove the color there, but I would prefer to do it in Illustrator.
Any thoughts out there?

Glad to be of assistance, Murrey (and Pete too).
I've been using this trick almost since masks were invented, so please forgive me for not explaining it too well. I thought it was so somehow common knowledge, but maybe I did discover it after all!
Maybe you knew it already, Murrey, but you can also make a mask out of live type. Just put it in front of your picture, select type and picture and Cmd+7.
Here's Snæfellsjökull again for Jacob's benefit. He seems to be an Iceland enthusiast!

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