Will bearded dragons die from being scared?

While it is unlikely that a bearded dragon's heart will suddenly give out due to fear, reptiles in general are highly susceptible to illness due to stress. Short, intense periods of stress are usually less damaging than prolonged stress over time. Stress certainly can kill reptiles.

To avoid overstressing your bearded dragon, ensure that it spends the majority of its time in its temperature-controlled enclosure, with access to appropriate hiding places. Keep handling sessions short, and extend them only as the dragon becomes tame and shows fewer signs of distress at being handled.

Signs of stress including struggling to escape, running away, or closing eyes and going limp. Dark color is also a sign of stress.