How to saw inground lumber
I would cut off the timber in the ground using a Sawzall type tool (reciprocating saw) that has a long rough cut blade installed. You can get blades as long as 12 inches that can easily reach into tight spots and cut the wood. Soil will wear the teeth away fairly quickly and so be prepared to replace the blade. 

I've used this technique to cut roots free from stumps when removing a tree. Works very well.