Short answer: there weren't any witnesses to the giant snake, but there were witnesses to the giant spider.
The important question to answer first is: who were these witnesses? The only two people we can be certain of are Tom Riddle, and Moaning Myrtle, but that gives us evidence enough:
We know that Tom Riddle got Hagrid expelled for keeping Aragog around (and scapegoated him as Slytherin's heir), and that Myrtle saw:
A pair of great big yellow eyes, watching me, over there.
Spiders have eight eyes, but two of their eyes are bigger than the others.
How is it possible to mistake a spider for a snake?
Myrtle had been crying, and wore thick glasses. She had also just been murdered by the gaze of a magical beast that was capable of petrifying multiple students 5 decades later.
The word of Myrtle alone would have been enough, but given that Riddle was a beloved student at Hogwarts, whose teachers were all said to be enamoured by, it's not surprising that it was easy to pin the blame on Hagrid. Additionally, it is said in The Chamber Of Secrets that the attacks stopped after Hagrid's expulsion, likely because Riddle was lying low.