What is the validity of Ibn Qutaybah's statement that it is permissible to order amputation without carrying it out, and can this be used as an argument against establishing the hudud punishment due to the lack of evidence that the Prophet (peace be upon him) ever carried it out?

One must avoid ambiguities, for they may settle in the heart and become difficult to remove.

The aforementioned hadith pertains to cutting off the hand of a thief, not a betrayer. The narrations have been reconciled to indicate that the reason for the cutting is theft, and the mention of the borrowed item was for identification, not as a reason for the cutting.

The hand of a betrayer is not cut off, as the Prophet, peace and blessings be upon him, said: "There is no cutting for a snatch-thief, nor for a plunderer, nor for a betrayer."

The Prophet, peace and blessings be upon him, did not pardon in matters of Allah's prescribed punishments; rather, he ordered their immediate implementation, as happened with the Makhzoomi woman who stole. This is why he became angry when Usama interceded for her.

"Cutting off" in the context of hudud (prescribed punishments) means the actual removal of the limb, not merely giving something or threatening. The literal meaning of a word cannot be diverted unless there is a clear impediment and indication, which is not present in the sacred texts.