In canto 1, Virgil speaks the following words to Dante (words that I think are useful in conceptualizing the larger tone and imagery bound together in Inferno):
follow me and I will be your guide
And lead you forth through an eternal place.
There you shall see the ancient spirits tried
In endless pain, and hear their lamentation
As each bemoans the second death of souls. (Inferno, transl. by John Ciardi, canto 1, lines 106-110)
Personally, I think the statement your question alludes to can be interpreted from two different (but also interconnected) perspectives. On the one hand, there is Dante's depiction of eternal damnation itself, shaped by this concept of contrapasso. We see, for example, those condemned for the sin of lust swept up and forever carried about in a storm (mirroring the intensity of their passions in life), while the gluttonous are forced to face the hunger of Cerberus. Consider, for one last example, the fate of thieves, whose very bodies they now must steal from one another.
One can imagine, in these various punishments, that these kinds of horrible experiences would have a destructive effect on one's sanity; moreover, note how these human souls are now, through the concept of contrapasso, forever defined by the sins and crimes that they committed in life. Essentially, in the act of damnation, they have forever become their sins.
The second key aspect to this question, I think, lies in traditional Christian understandings of sin and spirituality. According to Christian teaching, sin is endemic within the world, but it is also corrosive to the cultivation of virtue. Indeed, one can find examples of similar ideas outside of (and preceding) Christianity itself: Plato envisioned the philosopher's life as one lived in moderation, favoring neither hedonistic excess nor ascetic self-denial, and this same sense of moderation (and sometimes even asceticism) tends to play a major role in the Christian tradition as well: consider the importance of fasting, for example. Seen from this perspective, this loss of intellect would not necessarily be caused by the experience of damnation, but from the choices the sinners made in life. Rather than cultivating virtue or dedicating themselves to spiritual concerns, they cultivated their own baser impulses and instincts instead.