Among the several mature mulberry trees growing here, one was grafted on a dwarfing r/s and has really grown into an optimum shape needing very little pruning. I regret that I am not able to identify the r/s variety. The others all grow TOO verticle and TOO tall, so they get a lot of pruning to manage the size/shape. Generally speaking, these are being trained to develop several scaffold branches which will each grow new verticle shoots each year. The new verticle shoots are whacked off each Winter, except for a short stub with a couple buds to regrow new shoots in Spring.

SoTX,
Some selections, like Geraldi, are genetic dwarfs. Tissue culture - or even old-school methods, like rooting cuttings - don't alter that genetic determination; but tissue-culture will not induce dwarfing in a genetically non-dwarf clone.

Interesting that cwc has one on a dwarfing rootstock - I was not aware that there was such a critter in the mulberry world.
Many of the conventional 'dwarfing' rootstocks for pomefruits, etc. are dwarfing because they have 'weaker', less substantial root systems - hence the need to stake or trellis - and irrigate - trees on many of the true dwarfing rootstocks.
Perhaps someone has made such a selection out of the Morus genepool - though one might wonder if a rooted cutting - or even an interstem - of Geraldi or other 'dwarf' mulberry selection *might* confer dwarfing to varieties topworked onto them.

Some folks have advocated looping(tying an overhand knot in the limber trunk of a young whip) or bark inversion(cutting out a 1" strip of bark all the way around the trunk, turning it upside down and replacing it - as ways to induce (temporary) dwarfing and to initiate earlier flowering/fruiting.