See my article on the Oral Torah, pp. 63–72, for several approaches to resolving the problem:
https://drive.google.com/file/d/1mK1MZ7j0Y0fB5ljZpVqSw5beZZwIYuN6/view?usp=sharing
I especially expanded there on the possibility that the Jewish law changed between the generation of the wilderness and the Land of Israel (and more generally), and I showed quite a number of precedents for this from the Hebrew Bible (Tanakh) for anyone who does not deny the plain meaning of Scripture, such as the change in the law of the firstborn, the change in the laws of the priests in Ezekiel, and more. All this follows from the fact that the commandments are accepted laws and not statutes, as argued by Prof. Joshua Berman in his article.
And things along these lines were already written by the Malbim, who said that there is a hidden matter concerning the future renewal of the sacrifices, and by Meshekh Chokhmah, the Netziv, Rabbi Joseph Albo, the Kuzari, Rabbi Kook, Rabbi Yehuda Cooperman, Rabbi Sherki, and others. All this is in my article.

With God’s help, 25 Kislev 5779

From the fact that they are mentioned together — “and you shall give life for life, eye for eye…” — it implies that the punishment of taking a limb applies only when the injury was intentional, just as “life for life” applies only in a case of intent, since an unintentional killer goes into exile and is not executed.

Even in a case of intent, there is a need for two witnesses and prior warning in order to verify that the person really acted intentionally. And if even the punishment of lashes requires witnesses and warning, then all the more so this must be the rule for irreversible bodily punishments. So carrying out the punishment of cutting off a limb, according to the Torah’s strict laws of evidence, would be almost impossible in practice — and not for nothing is there no mention in Scripture of the actual implementation of an “amputation penalty.”

The Torah mentions, in certain cases, the possibility of redeeming a death penalty through ransom. Thus, regarding an ox known to gore that killed a person, about which it says “its owner also shall be put to death,” the Torah allowed redemption of the death penalty through “if a ransom is imposed upon him.” Only regarding a murderer does it say, “You shall take no ransom for the life of a murderer.” But in causing death through gross negligence, redemption through ransom is possible, and from this one may infer that even the punishment of cutting off a limb can be redeemed by ransom. And since in any case it is very difficult to prove “beyond a reasonable doubt” that the loss of the limb was done intentionally, redemption through ransom would have been the only practical possibility.

Best regards, Shatz Levinger
H

Although the duty of witnesses to give prior warning to the person in question is not explicit in the Torah as a condition for a guilty verdict, the witness’s obligation to warn is implied by his basic duty toward the transgressor: “You shall surely rebuke your fellow, and not bear sin because of him.” Since the witness did not fulfill his basic duty to rebuke his fellow, there is room for concern that the sinner was not aware of the severity of his sin. Even the credibility of a witness who did not fulfill his duty to rebuke is open to doubt.

Best regards, Shatz Levinger