The Oxford classics graduate also appears to launch a personal attack on Mr Griffiths himself, suggesting he is "stupid" and "not fit to be employed"
as the head of a body interested in Latin teaching.
The Cambridge Latin Course is used by 80 per cent of pupils learning the language and has its fans and critics across the teaching profession.
Mr Griffiths is considering taking legal action. He said: "Mount says there is not enough grammar in the course, which is nonsense. I wouldn't mind if what he was saying was accurate, but his statements are untrue. Our own research shows that it now contains more explicit teaching, practice and consolidation of more linguistic features than any other UK Latin course.
"It is very disappointing that he has created this distraction from the real task of getting more people learning Latin."
He added that the Cambridge Latin Course had managed to increase the number of non-selective state schools offering the subject in six years from 150 to 300.
Peter Jones, co-founder of Friends of Classics, a charity promoting the subject, said Mr Mount had made an "absolutely outrageous attack".
He said: "He is taking a very old-fashioned view. He is saying that if a pupil cannot learn it over 10 years in the complete and proper way in the classroom of a private school, it is not worth learning at all.
"But in modern state schools, pupils have to be able to tackle GCSE texts within two years, so inevitably some corners have to be cut. But the idea the Cambridge course doesn't teach grammar is not true at all. From his comments, you might think he hadn't read it at all."
Mr Mount refused to comment.