Firstly, we should respect and glorify the verses of the Qur’an and any papers containing Allah’s names and that of His Prophet Muhammad (peace and blessings be upon him). Almighty Allah says, [That (is the command). And whoso magnifies the sacred things of Allah, it will be well for him in the sight of his Lord.) (Al-Hajj 22:30)
Thus, if the books one has cannot be read or benefited from again, one is allowed to cut them into very small pieces, or burn them in order to save them from being misused or mishandled.
In his explanation on this issue, Sheikh Ahmad Kutty, stated:
If these books are Qur’an or valuable collections of Islamic literature, or general knowledge, and they can be repaired and used, then one should not worry about disposing of them; instead, they could be donated to a library while one is alive or one requests that this be done after his or her death. In this way, one will continue to reap the rewards of a sadaqah jariyah (ongoing charity) as long as they are available for people to benefit from.
If, however, they are not valuable, or they are beyond repair and re-use, one need to shred them before disposing of them, especially if they contain verses and texts from the Qur’an and hadith. If one has no access to a shredder, then the next best thing to do is to use scissors to cut them up in such a way that the Qur’anic verses and texts are unrecognizable. Then one can place them in recycling boxes. In this way, an obligation has been discharged.