The Qur’an mentions the purpose of administering the punishments it prescribes: 
    The purpose of the death penalty is to safeguard man's existence in this world: 

There is life for you in Qisas, O men of insight! that you may follow the limits set by Allah.(2:179) 

He who killed a human being without the latter being guilty of killing another or of spreading disorder in the land should be looked upon as if he had killed mankind altogether, and he who saved a human being should be regarded as though he saved all mankind. (5:32) 

    Amin Ahsan Islahi explains this in the following way: 

‘When the Qur’an says: ‘there is life for you in Qisas’, it is actually referring to the life of a society and not to the life of an individual. If a murderer is executed because of his crime, it apparently seems as if a second life has been taken, but a little deliberation shows that this punishment is actually a guarantee of the life of the whole society. If this punishment is not carried out, there is a strong chance that the mental disorder in which a person commits this crime is infectiously transmitted to the society. The extent of various diseases differs: diseases which result in such heinous crimes as murder, robbery, theft or fornication are like those diseases in which it is necessary to amputate some limb of the body to save the whole body. Amputating a limb may seam a callous act, yet a doctor has to be callous. If by showing sympathy to this limb he does not force himself to this cruelty, he shall have to bear with the patients death. 

A society in its collective capacity is like a body. At times, one of its limbs gets infected to the extent that the only option is to cut it from the body through an operation. If sympathy is shown by considering it to be the limb of a patient, there is all the chance that this would fatally effect the whole body.’ (‘Tadabbur-i- Qur’an’, Vol 1, Pgs 436-7) 

    In the cases of fornication, qadhaf and theft the purpose of the punishments is that besides being a grievous reward of the crime, the criminal be humiliated so that he becomes an example for the society. 
    In the case of fornication, the Qur’an says: 

And let a party of the believers witness their punishment. This man guilty of fornication may only marry a woman similarly guilty or an idolateress and this woman guilty of fornication may only marry such a man or an idolater. The believers are forbidden such marriages. (24:2-3) 

    About qadhaf, the Qur’an says: 

And never accept their testimony in future. They indeed are transgressors. (24:4)

    In the case of muharbah (waging war against Allah and His Prophet (sws)) and spreading disorder in the land, the Qur’an asserts: 

Such is their disgrace in this world, and in the Hereafter theirs will be an awful doom.(5:34)

    About theft, the Qur’an emphasises: 

As a reward of their own deeds, and as an exemplary punishment from God. (5:38)

    Islahi comments on this verse in the following manner: 

‘(In this verse) two reasons have been stated for the amputation of hands: firstly, it is the punishment of the crime, and secondly, the punishment has to be given in an exemplary way so that it becomes a means of a severe warning for others. The Qur’an uses the word nakal for such a punishment. Since both these reasons are stated adjacently without any conjunction between them, both of them must be regarded as essentials in carrying out the punishment i.e., a means of retribution of the crime and a means of a severe warning for the society. Those who do not simultaneously take into consideration both these aspects often end up thinking that the punishment is severer than the crime itself. The actual fact is that this punishment is not only the retribution of the criminal act, it is also a means to put an end to the many crimes which may be triggered as a result, if the criminals are not totally discouraged by treating them harshly. Like the craving for sex, the lust for wealth is equally intense in a person. If this lust is allowed to thrive and prosper, the consequences which arise may well be observed in our own society by any keen eye. If a list of crimes committed in the most civilised of countries in one year only because of theft is prepared, it will be enough to reveal the truth. The fainthearts of these civilised societies are deeply moved if hands are amputated because of theft, yet the horrendous crimes which result directly or indirectly through theft fail to rouse any feelings of concern in them. Theft is not a simple crime: it is a source of many crimes. If this crime is eliminated, these crimes shall automatically be taken care of. Consequently, it is a matter of experience that the amputation of hands on account of theft has not only reduced instances of this crimes, it has also gone a long way in reducing other crimes as well. If by amputating a few hands, the life wealth and honour of thousands of people are safeguarded then this is not a bad deal at all; in fact, it is a very lucrative one. Regrettably, our intellectuals fail to appreciate this.’   (Taddabur-i-Qur’an, Vol 2, Pgs 512-3)