It is difficult to know, some trees could change shape and going shrub-like, some will just continue, maybe with two tops, and some will not growth anymore.
All it depends on the species, and so about the ability to create new buds near cuttings or from roots, to make some secondary bods the new "main one" (but so often with two heads), or just not creating new buds. And then it depends on apical dominance: if new buds could create new branch which could become trunk (of just a disordered shrub).
Conifers are particularly difficult (and monocots e.g. palms, but they are not really trees): not many plan B and we like when they growth very regularly.
As you see, plants often have plan B, so possibly it will not die, but maybe you will never have a good shaped tree.
In any case: I always recommend to put a stick near every sapling, for mowers, for waling people, for snow/wind and for animals.