If it is a Zelkova (Zelkova serrata) it sounds like it had/has/is/was bittting the perverbial radish. Trunc suckers normally mean there is a problem with something or other. Pruning the dead out is a great option... But the tree is going to look like crap if you cut it in half like that. IMO.......... With out seeing it.......... Cut it down........ Replant a less maintenance intencive spieces. Zelkova form SUCKS. it is an up hill battle from day one. YOu cant get a central leader. Included bark everywhere. falling apart constantly. they shade thier inner branches out because they gettttt toooooo thickkkkkk. and one for all those lawn guys out there.... Grass dont grow well under them (no sun) go figure. Plant something native.