Saw them off, cut them off, shear them off and immediately paint the stumps with Brush B Gone straight from the container.
That way you limit your herbicide use to just the target.

thanks bambooo. my only concern there is that i've read that if roots are intertwined with desirable trees'/shrubs' roots, it could have an ill effect on them. i'll do some test spots and monitor the reaction. thanks again.

i hope you had great success as we have the same problem and i want help also. please send reply as to your results. thanks.

I posted my experience killing suckers from my neighbor's tree of heaven in another forum: link below.

Here is a link that might be useful: scroll down to read about the struggle

I unfortunately have a big one growing in my yard! I would love to cut it down but it is to expensive! I made the mistake of cleaning up an area behind my garage and have found hundreds of clusters of these things. In the 9 yrs we have lived in our house they haven't really grown back there. Now that I have disturbed them, they are growing all over my yard. I need to know how to kill the clusters while they are still in the ground, because digging them up is not an option?