Stoning and amputations are hadd punishments that Allah has prescribed for His slaves, in accordance with His wisdom and out of mercy towards His slaves

Praise
be to Allah

Firstly:

Allah has prescribed the hadd punishments in order to protect
the limits which He has forbidden us to transgress, and so as to protect the
rights of His slaves which He has enjoined are to be protected, and as a
means of expiation and purification for those who commit the deeds in
question. He has ordained that as part of religion so as to know who truly
believes in Him and His laws, and will hear and obey, as distinct from those
who pay no attention to that and do not see anything wrong with
transgression of the limits set by Allah, and He has made it as a deterrent
to those who are tempted to transgress the sacred limits set by Allah.

Secondly:

The Prophet (blessings and peace of Allah be upon him)
carried out stonings and amputations.

With regard to stoning: Al-Bukhaari (6830) and Muslim (1691)
narrated that ‘Abdullah ibn ‘Abbaas (may Allah be pleased with him) said:
‘Umar ibn al-Khattaab (may Allah be pleased with him) said, when he was
sitting on the minbar of the Messenger of Allah (blessings and peace of
Allah be upon him): Allah sent Muhammad (blessings and peace of Allah be
upon him) with the truth, and He revealed the Book to him. One of the things
that Allah revealed to him was the verse of stoning. We recited it,
memorized it and understood it, The Messenger of Allah (blessings and peace
of Allah be upon him) stoned [adulterers] and we stoned them after him. But
I am afraid that with the passage of time, people will say, we do not find
stoning in the Book of Allah, so they will go astray and forsake an
obligation that Allah revealed. Stoning (is mentioned) in the Book of Allah
as a duty which much be carried out on those who commit zina if they are
married, men and women alike, if proof is established or if there is
pregnancy or a confession.

Muslim (1692) narrated that Jaabir ibn Samurah said: I saw
Maa‘iz ibn Maalik when he was brought to the Prophet (blessings and peace of
Allah be upon him), a short, well-built man who was not wearing a rida’
(upper garment). He testified against himself four times, saying that he had
committed zina, and the Messenger of Allah (blessings and peace of Allah be
upon him) said: “Perhaps you (kissed her or embraced her)?” He said: No, by
Allah, this ignoble one has committed zina. So he stoned him…

 Ibn al-Qayyim (may Allah have mercy on him) said:

Those whom the Messenger of Allah (blessings and peace of
Allah be upon him) stoned for zina were well known and few in number, and
their stories were recorded and are well-known. They were the Ghaamidi
woman, Maa‘iz, the woman who committed adultery with the hired worker, and
the two Jews.

End quote from at-Turuq al-Hukmiyyah (p. 53)

With regard to amputations, the Prophet (blessings and peace
of Allah be upon him) cut off the hand of a male thief and a female thief.

Al-Bukhaari (6788) and Muslim (1688) narrated from ‘Aa’ishah
(may Allah be pleased with her) that that Quraysh were concerned about the
case of the woman who had stolen, at the time of the Messenger of Allah
(blessings and peace of Allah be upon him), during the conquest of Makkah.
They said: Who will speak to the Messenger of Allah (blessings and peace of
Allah be upon him) concerning her? Then they said: No one would dare to do
that but Usaamah ibn Zayd, the beloved of the Messenger of Allah (blessings
and peace of Allah be upon him). She was brought to the Messenger of Allah
(blessings and peace of Allah be upon him), and Usaamah ibn Zayd spoke
concerning her. The colour of the face of the Messenger of Allah (blessings
and peace of Allah be upon him) changed, and he said: “Are you interceding
concerning one of the hadd punishments of Allah?” Usaamah said to him: Pray
for forgiveness for me, O Messenger of Allah! When evening came, the
Messenger of Allah (blessings and peace of Allah be upon him) stood up and
delivered a speech. He praised Allah as He deserves to be praised, then he
said: “Those who came before you were doomed because, if a nobleman among
them stole, they would let him off, but if a lowly person stole, they would
carry out the hadd punishment on him. By the One in Whose hand is my soul,
if Faatimah the daughter of Muhammad were to steal, I would cut off her
hand.” Then he ordered that the hand of that woman who had stolen be cut
off.

And it was narrated from Safwaan ibn Umayyah that a man stole
his cloak, and he was brought to the Prophet (blessings and peace of Allah
be upon him), who ordered that his hand be cut off. He [Safwaan] said: O
Messenger of Allah, I let him off. He said: “Why did you not do that before
you brought him to me, O Abu Wahb?” and the Messenger of Allah (blessings
and peace of Allah be upon him) cut off his hand.

Narrated by Abu Dawood (4394) and an-Nasaa’i; classed as
saheeh by al-Albaani in Saheeh an-Nasaa’i.

Thirdly:

The claim of the one who says that throughout the history of
the Islamic caliphate, until the end of the ‘Abbaasid caliphate, only nine
people had their hands cut off for stealing is not correct at all. This
statistic cannot be proven, because of the expansion of Islamic territory
and the large number of countries and regions. It is not possible to have a
record of everything that happened in all these lands, throughout this
lengthy period, and we do not know that historically the caliphs and their
governors used to record the number of amputations done as hadd punishments
for stealing in every city, small or great. This is something that cannot be
known, let alone to say that they were all counted and the number was nine!

What is definitely known is that the number of people whose
hands were amputated as the hadd punishment for stealing during this period
was much greater than that.

This is a view that should not be given any attention and
should not be relied on

Moreover, what does the one who says that mean by it, when it
is proven in the Book of Allah and the Sunnah of His Messenger (blessings
and peace of Allah be upon him), and none of the leading scholars of Islam
differed concerning the fact that it is obligatory?

For more information, please see the answer to questions no.
9935 and 14312

And Allah knows best.