If it is a weeping dissectum (and most dissectums ARE weepers), then it is entirely natural for the branches to hang down. They will grow straight out for a short distance, then become pendulous or weep or cascade. These do have the appearance with maturity of an umbrella or mushroom shaped shrub - that is just the way they grow.

The photo of Mike's (Botann's) tree may be somewhat misleading as it is taken from below looking up and the size is deceptive. You can gradually remove lower branching to create more of that domed look but it is best to allow the tree to develop and mature some before attempting to remove much growth. Staking young dissectums also will increase more urpright, vertical growth but the branches will still cascade.

It would be helpful to post photos of the tree in question to get more definitve suggestions for pruning. With any Japanese maple and pruning, remember that less is more :-) The best and most successful pruning to enhance the growth habit of any JM is something done gradually and incrementally over an extended period of time.