Hi Mac

The Mulberry bleeds white sap, yes that's normal, branches mostly and
the cambium some.
If you go to my website there are some mulberry turnings in there.
I like turning Mulberry, it is related to Osage Orange (bois d'arc or
bow wood or bodark)
The heartwood is a nice shimmering Yellow and the sapwood almost white,
cuts good and finishes nice, however the sapwood shrinks more (a lot)
than the heartwood, so you have to keep that in mind when rough
turning, really slow down the drying or it will check even the
heartwood, (seal it and bag it) or turn it THIN.
So for your smallish branches I would go natural edge and thin, CA the
bark as soon as done shaping the outside then complete, no coffee break
G.
Chatoyance on the finished bowl, platter, etc. really makes it
worthwhile turning wood.

http://homepage.mac.com/l.vanderloo/PhotoAlbum26.html

Have fun and take care
Leo Van Der Loo