How can meteorites cause catastrophic extinction?
I would say through the induction of an extended global winter.
One way (apart for the obvious mechanic effect of the impact causing a huge explosion and consequent death in the range of the explosion) that a meteorite can cause a widespread extinction is the production of a "forced winter" effect.
The dust lifted by the impact of the meteorite can reach the upper-troposphere and stratosphere where it will stay for a long time because there will not be rain to make it come back to the surface of the Earth. This dust will gradually cover the entire planet and form a kind of a shroud of dust that will absorb/reflect solar radiation cooling the surface of the Earth underneath.
This cooling and lack of Sun radiation will be quite severe, causing the death of plants and animals depending from the Sun for survival (reptilians, for example). The death of plants will affect plant-eating animals that will die as result (after a while) causing the death of the carnivores that feed on them as well!!! In the seas, phytoplankton (microscopic plants) will die for lack of Sun radiation. Zooplankton, feeding on phytoplankton, will disappear next. The rest of the food chain will then disappear as a consequence (Wales for example feed on plankton) leaving a lifeless sea.
[A localized "impact-like" dust cloud caused by a volcano]
You can see some of these effects (such as localized lowering of the temperature and darker days) after the eruption of the volcano Krakatoa (1883).