What's the easiest way to cut a chunk out of a buried railroad tie?
I've used a sawzall type reciprocating saw with the 14" long demolition style blades for similar type wood removal in the ground. 

Be prepared to replace the blade a few times as cutting into dirt can mess up the teeth after a while. 

With the saw like this you should be able to cut completely through the old timber without having to do any chiseling in the hole. Just enlarge your hole enough to give access to permit cutting the wood back far enough so that it does not interfere with your pier form.