Deleting Qur'an from a smartphone, tablet or computer is a tricky question.
The ruling of deleting the Qur'an app from a phone or a file from the computer would depend on the intention of the person. If the person deletes the Qur'an with a wrong intention such as disrespect of Qur'an, erasing the Qur'an from the heart and mind, etc.... then it would be Haram and it would also affect the faith of this person negatively.
If someone deletes the Qur'an from their phone or computer simply because they are going to replace it with a newer version or better file/app then there is absolutely no harm. Likewise, if someone was deleting an app of Qur'an that he does not use anymore or due to storage issue, etc.... then there is no harm.
And Allah knows best.
Mufti Ikram ul Haq
Fatwa Center of America