I am working on a tree stump cake where the outside is chocolate buttercream. For the life of me, I can't wrap my head around how I'm going to do the little heart shaped cut out with the initials. Chill it and then try to scoop out the area where the heart would be, followed by filling it back in with a lighter color? Does anyone have any other ideas or does this sound about right?

that's about right -- or you could scoop a bit and stick in a fondant heart -- 

or you could put down some lighter icing -- ice it in chocolate -- maybe fridge it in between then when you scoop you're already there

and the cool thing is you don't have to bother about smoothing it out because it is supposed to look carved so a few wrinkles will add to the effect bravo!

If I'm understanding your ? right I suggest using a very thin frozen b'cream transfer.  Spread b'cream on plastic wrap, fz then 'paste' over the chocolate and as it thaws, carve in the letters. 

Yes!! Both of these ideas are fantastic!! Thank you so much!

I would crumb coat (rather heavily at least in the heart area) with a pale white-tan color, take a heart shaped cookie cuter and stick it into the side of the cake where the initials will be and frost with the chocolate frosting around the cookie cutter.  As -K8memphis said, the icing is not supposed to be smooth, so it doesn't have to be applied all the way around with a bench scraper.  Hope that makes sense????

It does! Thank you SandraSmiley :-)