In my opinion the purpose of Clarisse's death was three-fold.
1. Clarisse had to die because she was all that remained of what we readers understand as good. This is a dystopian novel. Thus, for us to find the society as completely dysfunctional, we needed to see that one lasting piece of truth and goodness destroyed. This spurs our passion to act once the reading is done.
2. Clarisse's death only further perpetuates the motives of Montag to seek out and either liberate the society or himself from the society. When he learns of the typical way she might have died, it enrages his drive to continue his journey.
3. This is a little off topic, but I think very relevant. My students often read into Clarisse as a potential love interest for Montag. For her to have continued to exist, readers might lose sight of what Bradbury was really trying to point out. He had no intention in commenting on romance and how it develops. His intentions had to do with making society think about the fact that technology and the absence of reading can destroy us unless we are careful.
Because she dies... She was killed by a car that ran her over