All perfect praise be to Allah, The Lord of The Worlds.
Islam is the religion of mercy and forbearance, and Almighty Allah has sent Prophet Mohammad (PBUH) as a mercy for all creatures where He said{What means}, "We sent thee not, but as a mercy for all creatures"{Al-Anbia`, 107}. Therefore, this mercy includes all creatures; not only man and animals.
Sharia scripts teach that Allah has prescribed kindness and forbearance in everything, including animals, since the Messenger of Allah was reported to have said, "A woman got into Hell-Fire because of a cat whom she had tied, and thus it could not eat, and she did not let it free so that it could devour the vermin of the earth, until it died."{Related by Bukhari}. He (PBUH) also said, "While a man was walking he felt thirsty and went down a well and drank water from it. On coming out of it, he saw a dog panting and eating mud because of excessive thirst. The man said, 'This (dog) is suffering from the same problem as that of mine. So he (went down the well), filled his shoe with water, caught hold of it with his teeth and climbed up and watered the dog. Allah thanked him for his (good) deed and forgave him." The people asked, "O Allah's Messenger ()! Is there a reward for us in serving (the) animals?" He replied, "Yes, there is a reward for serving any animate."{Related by Bukhari}.
Therefore, in principle, it isn`t permissible to kill dogs. However, this excludes the voracious dog which threatens people`s life and property and spreads terror amongst members of society; particularly children. It is permissible to put such dog down if there is no other means to prevent its harm and it isn`t possible to send it to dogs shelter. This ruling is based on the Hadith in which the Messenger of Allah said, " Five are the vicious and harmful things which should be killed even within the precincts of Haram: rat, scorpion, crow. kite and voracious dog."{Bukhari & Muslim}.
However, certain conditions should be met in order for killing a voracious dog to become permissible: It isn`t owned by anyone, if it is then the owner should be asked to prevent his dog from harming people. Its harm can`t be stopped save by putting it down. This in addition to observing Ihsan (Perfection) when killing it: it shouldn`t be mutilated nor tortured before it is killed, because it is being killed to prevent its harm, and not for vengeance. Anawawi (May Allah be pleased with him) said, "Voracious and rabid dogs should be killed, as indicated by the Prophetic Hadith in which the Messenger of Allah said, " Five are the vicious and harmful things which should be killed even within the precincts of Haram: rat, scorpion, crow. kite and voracious dog."{Bukhari & Muslim}.
However, it isn`t permissible to kill non-voracious and non-rabid dogs, be they useful or not, black or not; as agreed by all our fellow scholars.
Imam al-Haramain Al-Juwaini said, "The order to kill the black dog and other ones is abrogated, so it is unlawful to kill any of them, except the voracious and the rabid."{Al-Majmou`, 9/235}.
However, if the dog`s harm is limited to barking and damaging property, then, in principle, it isn`t permissible to kill it. Rather, other means should be resorted to, such as banishing and scaring.Today, organizations could be established to care of these dogs.
As for nullifying one`s Wudu`(Ablution), scholars are agreed that touching a dog or any part of it doesn`t nullify ablution, because there is no legal evidence supporting such a thing, and this is why this wasn`t mentioned amongst the nullifiers of ablution. In principle, a dog is Najis(Impure/unclean)-its saliva, urine or sweat-as indicated by Shafie and Hanbali scholars.The transmission of this Najasah(Impurity) varies according to whether the dog is wet or dry. If it was wet and contacted that which is wet or vice versa, then the affected part is what becomes impure. To remove this impurity, the affected area should be washed seven times, one of them with earth. However, if both the dog and the person touching it were dry, and none of the dog`s saliva, urine or sweat has reached him, then there is no need for that person to take a ritual bath. This is since no impurity is involved, and this is reflected in the Sharia maxim which states: "When what is pure and dry comes in contact with what is impure and dry, it isn`t rendered impure." Al-Sayooti states, "Al-Qhamooli said in "Al-Jawahir" " When what is pure and dry comes in contact with what is impure and dry, it isn`t rendered impure."{Al-Ashbah Wa-Al-Natha`ir, 432}. Hanafi scholars have limited a dog`s impurity to the situation where a dog licks a utensil. This is in addition to its saliva, urine and sweat. Kindly refer to "Tabyyeen Al-Hakaa`ik Shareh Kanz Ad-Dakaa`ik, 1/30} by Fakhir Al-Din Al-Zaila`e.
On the other hand, Maliki scholars said that a dog is pure as long as it is alive, and this also applies to its saliva, urine and sweat. Kindly check Hashiyat Al-Sawi Ala Al-Shareh Al-Sagheer, 1/43} by Al-Dardeer.
In conclusion, it is worth pointing out that the opinion of the majority of scholars about dog`s impurity is fixed, and it isn`t permissible to kill the dog or mutilate it under the pretext that it is impure. Rather, it suffices to wash off the impurity. And Allah the Almighty knows best.