There is no reason to put him down...this horse is acting as if he were a stallion because due to some testicular tissue leftover, he thinks he is. Would you put a stallion down if he acted this way? If so, there are going to be a lot of stallions euthanized because they all act that way at some point in time in there lives.
I highly recommend you look into following Clinton Anderson's Downunder Horsemanship. It is an excellent training method for any horse, but especially problem ones. For now, whenever he behaves badly make him back up. First teach him how to back up and when he is naughty really get after him. Horses do not LIKE to back up (do you ever see one in the pasture randomly backing?) No. Carry a short dressage whip with you and whenever he is naughty really make him back, back, back, back, back....and make him do it quickly. Trust me on this tried and true method. He will soon learn to behave himself because it is no fun to have to work so hard. If he won't back, use the whip on his chest. Whatever you have to do to get him to back (don't beat him, but mean business) make sure you make it clear that he needs to get out of your space and that this is a punishment for the behavior he is displaying. I typically make my naughty horses back 10-20 steps very quickly...then go forward again and act like nothing ever happened...if he's naughty again, then repeat the punishment. You may have to do it many times, but eventually he WILL figure it out. Anytime he displays a behavior you don't like, you make him back. It is different under saddle. I do not make my horses back under saddle much because when they learn something new (dressage), if they know how to back, then tend to back up if they get confused. Reinback is in 2nd or 3rd level, so no need for a training level horse to know how to back. If he is naughty under saddle, do a one rein stop (nose to your knee).
For more info, research Clinton Anderson and consider becoming a member and purchasing the videos :) Good Luck!