Plumbing – Removing cartridge from mixer tap – recessed nut

You should be able to turn the body of the angle-stop if the nut is held firm with another wrench. if you turn the body and not the nut - It is less likely to damage the copper tube. Depending upon how tight the nut was set - will determine how deformed the copper pipe is. sometimes it is difficult to remove the ferrel.

You have so much oxidation on this valve - I would replace it.
Personally, I never install an appliance onto an old valve.

It looks like you have enough room to cut off the entire angle stop. Use a fine toothed metal blade and cut square - then deburr. A new multi angle stop can then be used with the matching outlets you need. The braided dish washer supply lines come in different configurations. I have found that many of the new dishwashers have a large threaded connector instead of the older 1/4" compression. check yours.

P.S. check inside your pipes for pitting. Often this oxidation can be a result of iron in water which destroys copper pipe.

Clean off mineral deposits with a brass or steel brush and a lime dissolver such as CLR or Limewaway. Towel dry as much as possible. Dry further with hair dryer in an attempt to evaporate as much moisture as possible; this, to leave room for penetrating oil to penetrate.

Aply penetrating oil such as PB Blaster or Liquid Wrench. Tap, tap, tap the the valve to set up vibrations to encourage the penetrant. A vibrator can be useful to assist, such as an electric tooth brush or electric engraving tool. Allow penetrant to sit for hours and tap some more after that.

Use a tight fitting wrench or possibly a pipe wrench to turn it anti-clockwise.