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The leaves can fall off your smoke tree for several reasons:
too much, or too little water
insect or disease damage
damage to plant by weed-eaters or mowers
age of tree
too acidic soil

You can test the branches, if they snap and break they are likely dead. Bending branches and if you scrape the bark and it is green underneath there is still life in the tree.
The stress of to much rain may have weakened the plant.
Did you inspect for any signs of insect or disease?
Your tree was likely a grafted tree, meaning the rootstock is of a different cultivator than the tree. You can let the shoot grow but it will likely be a different tree than the original.
Sometimes there is just no explanation for the death of an established tree. You can remove the tree now, or wait until spring.

Losses in the garden make for new opportunities!

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

Smoke Bush does grow in most soil conditions, though if your clay soil is not well draining, this is likely the issue.

Smoke Bush prefers a full sun location though they can tolerate partial shade.
Make sure when you dig the planting hole that you dig it twice as wide as the root ball and you can add some organic compost to the bottom of the planting hole.
Make sure the tree sits slightly above the soil line. If planted to deeply the plant may suffer.
Make sure you are in the appropriate zone to grow Smoke Bush.
Most cultivators are hardy in zone 5 - 8, 'Royal purple' is listed as zone 4 hardy.

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

Smoke trees tend to have a rangy, splayed growth habit which is why annual pruning is important to keep it more compact and to strengthen limbs.

For more information on trimming smoke trees, please visit the following link:
https://www.gardeningknowhow.com/ornamental/trees/smoke-tree/pruning-smoke-trees.htm

I would follow the planting instructions that were included with your tree.
Soaking bare roots is a general recommendation and helps to hydrate and wake up the roots.

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

The bark of a Smokebush is susceptible to breaking and damage.
Dead branches can be pruned away now, but regular pruning should take place in early spring or late winter.
Here are some articles to help you.

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