This Amnesty International page on the death penalty laws in Saudi Arabia notes the following:
The absence of a debate on the death penalty cannot be attributed to Islam or Shari'a rules, because the works of Muslim jurists are full of interesting debates on crime and punishment, including the death penalty, which is reflected in the diversity of penal policies and practices in different Muslim countries. In Saudi Arabia, the fundamental reason for the absence of any debate on the death penalty is due to the threat of the imposition of the death penalty itself, in that anyone other than the state taking the initiative to start a debate risks being categorised as apostate or as ''corrupt on earth''. This is so because religion and politics are the ownership of the state. Dissent, be it religious or political, can easily be seen as ''corruption on earth'' or a deed harmful to the unity of the nation, and both of these acts can be categorized as capital offences. This is why Saudi Arabia has no political parties, trade unions or even a bar association. Given these factors, as well as the government's harsh penal policy, linked as closely as it is to religion, a debate on the death penalty in Saudi Arabia seems a distant aim.
I am told that a similar situation exists with regard to the blasphemy law in Pakistan. To criticize the law is to risk being guilty of blasphemy.