I'm seeing that too. It may be a euphemism, but I think it's worth adding.

@@ -15,0 +16,5 @@
+<sense>
+<pos>&n;</pos>
+<pos>&vs;</pos>
+<gloss>carrying out a sentence (e.g. execution)</gloss>
+</sense>

ejje.weblio
死刑制度を復活させて、源為義らを処断した。
The death penalty was resumed and MINAMOTO no Tameyoshi was executed.
その書状には成幹の処断を指示する内容があった。
In the letter was an order to kill Narimoto.
「であるから、信康が信長の処断要求に乗じた家康の命令で処断されたことに、数正は強い憤激を覚えていたはず
である。」
Kazumasa was therefore outraged that Nobuyasu had been killed by Ieyasu on Nobunaga's order.

I'm seeing various examples that translate 処断 as execution or death sentence, but I don't see 
that definition in the kokugos. Am I missing something?