I am not sure about mulberry , but usually with deciduous trees you take cuttings when the tree shed it's leaves and is dormant.

I planted mulberry tree this year and it came grafted.
I think that in order to get a strong tree you need the roots from one tree and the fruits from a different tree.

If this is so, it's best to get one from the nursery.
It will grow much faster.
the one i got was a meter in height, and now just a few months after i planted it, it's over three meters.