The Oort cloud of comets was formed by the ejection of icy planetesimals from the region of giant planets--Jupiter, Saturn, Uranus and Neptune--during their formation. Dynamical simulations have previously shown that comets reach the Oort cloud only after being perturbed into eccentric orbits that result in close encounters with the giant planets, which then eject them to distant orbits about 10(4) to 10(5) AU from the Sun (1 AU is the average Earth-Sun distance). All of the Oort cloud models constructed until now simulate its formation using only gravitational effects; these include the influence of the Sun, the planets and external perturbers such as passing stars and Galactic tides. Here we show that physical collisions between comets and small debris play a fundamental and hitherto unexplored role throughout most of the ejection process. For standard models of the protosolar nebula (starting with a minimum-mass nebula) we find that collisional evolution of comets is so severe that their erosional lifetimes are much shorter than the timescale for dynamical ejection. It therefore appears that collisions will prevent most comets escaping from most locations in the region of the giant planets until the disk mass there declines sufficiently that the dynamical ejection timescale is shorter than the collisional lifetime. One consequence is that the total mass of comets in the Oort cloud may be less than currently believed.