Sort:  

Is it suckering (sending up new shoots from the bottom)?

What? I don't know what you mean.

Can you take a picture of it for me sometime soon so I can give you accurate advice?

That is a beautiful tree. Does it have a single trunk or multiple? You may have two options for getting of them from that one tree.

It is a single trunk tree.

Do you have a dormant season there (winter) when the tree is not actively growing? That would be the best time to attempt propagation.

I'm in the southeast United States. The Winter season starts in November. I heard some guys say we are in Zone 5. I don't know if that is helpful or not.