Well, in the personificated picture that we often have of particles, it indeed ceases to exist. In a less dramatic language this can also be described on the level of fields: electron in the atom is a localized Dirac field while the incoming photon is an EM wave. This process is then morally no different from classical theory of interaction of waves with matter: some of the wave is reflected, some is scattered, some is absorbed.
Similarly, one could ask a question similar to yours about the creation of particle-antiparticle pairs. Are these brought into existence by some act on magic? It turns out that on the level of fields these are nothing else than quantum mechanical fluctuations that you can imagine as ripples and peaks on the sea surface. The sharp peaks then essentially have properties of particles. Indeed, this is how we think of particles in general: they are well-formed local portions of the field.