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This can come back. It will just come back as a multi trunk tree. If you only want one trunk you will have to cut back all but one. It is best to install fencing around trees until they are established enough to fend off an attack such as this.

Despite all that rapid growth, the flowers may not appear until the plants are 15 years old. A relatively tall tree can still be too immature to bear blooms. When the flowers finally do appear, they bloom high up in the tree and may not be visible with the naked eye. If the tree appears to have no blossoms, examine the branches through binoculars to locate hard-to-spot blooms.

https://www.gardeningknowhow.com/ornamental/trees/tulip-tree/growing-tulip-trees.htm

Assuming you are referring to tulip tree, sometimes called tulip poplar (Liriodendron tulipifera) and not tulip magnolia, or African tulip tree:
http://www.missouribotanicalgarden.org/PlantFinder/PlantFinderDetails.aspx?kempercode=a878

--they are a very large growing tree, with a mature trunk diameter of 2 feet in 20 years possible, and 3 feet or more in 40 years. And yes, the roots, in time, would almost certainly lift a walkway even 4 to 6 feet away or more. They are beautiful, but need plenty of space.

This ornamental requires little pruning except to remove dead, damaged or crossing branches. You also can lightly prune to shape or prune harder to rejuvenate or promote more vigorous growth. The ideal time to prune is after the tree flowers in early spring.
Topping a tree is never recommended.
Flowering occurs in the spring.

If you are referring to the North American tulip tree (Liriodendron tulipifera) and not tulip magnolia, then you have the wrong tree in the wrong place. They grow to 50 meters in their native habitat. To hope to keep it 12 feet in height is unrealistic and would require extreme and detrimental pruning practices that would not be possible to sustain in the long term.

If the tree is a tulip magnolia then it still would be severely limiting natural form and beauty, but maybe more realistic than trying to miniaturize the tallest North American hardwood tree.

Absolutely! The cutting that you take will be the same age as the tree that it came from. This article will help you with taking cuttings: https://www.gardeningknowhow.com/ornamental/trees/tgen/how-to-root-cuttings-from-various-shrubs-bushes-and-trees.htm