Red giant might be impossible, but a collision with a white dwarf could kill a star. But I think the most likely result would be a supernova and a neutron star remnant. The mass limit is only 1.4 solar masses after all. I guess you could assume either a low mass white dwarf or a collision with high enough energy to blow off much of the mass of the sun. In any case the addition of the white dwarf would allow the composition of the sun to change relatively fast and it would add heavier elements and probably blow off significant amount of hydrogen, so it would drop the lifespan.
Downside of this solution is that the "special effects" would be spectacular, quite deadly, and entirely different from the red giant you asked for. The energy released on impact would be quite lethal and even a near miss by a stellar mass object would alter planetary orbits. But if that is okay...
Actually, maybe a near miss by a stellar mass object causing the Earth to be propelled out of the solar system would be close enough for your needs. Watching as the sun shrinks in the distance and atmosphere freezes would be very close in effect to sun dying.