Honestly, you guys don't understand the disservice that you are doing by posting online that someone should cut tree of heaven.
Never cut tree of heaven, because it will spread so quickly it will make your head spin. It is horribly invasive. For trunk diameters greater than 6 inches, treat it by hack and squirt using straight triclopyr 3. For diameters less than 6 inches, you can treat it by basal treatment (spraying on bottom 15 inches of the trunk) using triclopyr 4 diluted with diesel fuel or crop oil at a ratio of 1 to 4.
I have never seen signs of deer eating actual tree of heaven on my farm. Tree of heaven closely resembles sumac, which deer love, and I wonder if people get the two trees confused.
Don't take my word for it, just Google tree of heaven and you'll soon find out how nasty it is.