How is God's mercy manifested in the Hadd penalty of execution by beheading, even though the questioner accepts God's prescribed penalties and believes them to be the truth, yet her soul finds it difficult and she cries upon witnessing it?

Your submission to Allah's ruling regarding retaliation (Qisas) is a sign of your faith. Your emotional reaction upon witnessing Qisas does not affect your faith, as long as you are submissive to it and believe in it. Indeed, a Muslim must surrender to the fact that all of Allah's rulings are just and wise, as He Almighty said: "And the Word of your Lord has been fulfilled in truth and in justice. None can alter His Words, and He is the All-Hearer, the All-Knower." Your view of Qisas is limited, for wisdom dictates the killing of thein who aggressed against a life and spread fear, otherwise chaos would prevail. Moreover, Qisas preserves the life of society because it deters killers. Allah Almighty said: "And there is for you in Qisas [retribution by equality] preservation of life, O you [people] of understanding, that you may become righteous." Qisas is a deterrent against the crime of murder, unlike imprisonment, which does not deter people, thereby increasing the depletion of society through widespread killing.