I shall begin by saying that I'm not an organic chemist, so take what I say with a pinch of salt... Hopefully a proper organic chemist will provide a response shortly, but I felt that as this is your first post, it would be good for somebody to respond - if only so that you know that somebody read it!
I have never worked with wood tar, but I would imagine that it is a pretty complex mixture of hydrocarbons. With this in mind, there should be plenty of non-polar solvents that would dissolve (at least the bulk of) your material. Personally, I would consider experimenting with something like dichloromethane, hexane or similar. This should at least get your tar into solution. Assuming it dissolves, removal of amines could (in theory) be done by changing the conditions such that your amines become water soluble and thus partition into an aqueous solvent such as water. There are a few ways this could be done...
From what I remember of my organic chemistry (a long time ago) smaller amines can be removed by the addition of copper sulphate solution. The addition of this forms copper-amine complexes which are water soluble. You end up with 2 layers, an organic layer containing your tar compounds and an aqueous layer (which from memory forms an nice deep blue colour) containing your small amines along with anything else which is (or becomes) water soluble. You know when you're done when the blue colour no longer forms. I think that this only works with smaller amines, so might not be appropriate with the amines that you have. Alternatively, you could add dilute hydrochloric acid which should protonate your amines (and potentially other stuff) thus making them water soluble. The basic process of liquid liquid extraction is covered in the video linked to below:https://www.youtube.com/watch?v=TL0ZsNHGhsc
Might be worth trying this on a small scale to begin with!