That guy that stabbed four people to death on the MRT is still going to get the death penalty (death sentences upheld by high court, article in Chinese).
From Wikipedia, here is how capital punishment goes down in Taiwan:
Executions are carried out by shooting using a handgun aimed at the heart from the back, or aimed at the brain stem under the ear if the prisoner consents to organ donation. .... Executions are performed in secret: nobody is informed beforehand, including the condemned. The execution chamber is located in the prison complex. The condemned is brought to the chamber by car and pays respect to the statue of Ksitigarbha located outside the chamber before entering. Before the execution, the prisoner is brought to a special court next to the execution chamber to have his or her identity confirmed and any last words recorded. The prisoner is then brought to the execution chamber and served a last meal (which includes a bottle of kaoliang). The condemned prisoner is then injected with strong anaesthetic to render him or her completely senseless, laid flat on the ground, face down, and shot. The executioner then burns votive bank notes for the deceased before carrying away the corpse. It is customary for the condemned to place a NT$500 or 1000 banknote in their leg irons as a tip for the executioners (emphasis mine).