Why is the vibrational kinetic energy of a body ignored when calculating the total kinetic energy? In calculating the total kinetic energy of a macroscopic rigid body, we add the total translational kinetic energy and the total rotational kinetic energy of the constituent particles. Why is the total vibrational kinetic energy of the constituent particles left out?
 A: A net force or torque on a rigid body will not affect its internal energy. As it remains constant before and after the application of the force/torque, it is not relevant to the equations of motion.
A: 
we add the total translational kinetic energy and the total rotational kinetic energy of the constituent particles. Why is the total vibrational kinetic energy of the constituent particles left out?

We don’t actually leave out vibrational kinetic energy if the centre of mass of the system is vibrating.

This is a matter of scales at which you’re analysing the system. If you’re interested in the mechanics of the system, then you can get away with treating most solids as a rigid body where there is no relative motion between its constituents.
At this point I’d like to point out that for a multi-particle system, it’s convenient to decouple the motion as a centre of mass rigid body motion and “internal” motion about the centre of mass. The dynamics of the centre of mass is described by Newton’s laws. If the number of constituent particles is small, we can sort of get away with using Newton’s laws itself for the internal motion. But for the description of the internal motion of a large number of constituents, we need a different kind of dynamics. This is what we call thermodynamics, or more precisely, statistical mechanics.
Here comes a concept known as the equipartition theorem which says that if we are at thermal equilibrium, then the energy of each kind of motion (translation, rotation, vibration) usually known as degrees of freedom, contribute equally. So you see, vibration is as relevant and equally represented as the other kinds of motion.

In a comment in another answer you have asked:

If friction acts on the body, the internal energy changes. Yet, even in the presence of friction, the vibrational kinetic energy is not included.

We actually do have to consider all possible degrees of freedom. The energy is equally distributed to or taken from all of them. But as I said earlier, we rarely talk about internal energy when we are concerned with the macroscopic dynamics of a mechanical system.
A: Because the definition of rigid body requires that the distance between its points doesn't change. If we follow that model, only translations and rotations are possible.
If we modify the model from a rigid body to an elastic body, mechanical vibrations are included.
For a more complete description, heat transfer must be also included, resulting from external friction for example, and internal friction, as damping of mechanical vibrations, or even plastic deformations.
