You are leaving several key points.

1. a person that has been sentenced to death was convicted beyond a reasonable doubt of a crime by a jury of their peers. Thus, they are not a victim but a criminal.

2. They had an appeals process which they could avail themselves of and the execution only proceeds after that process has been exhausted. Thus, an execution of a prisoner sentenced to death is not in cold blood.

3. The two are unrelated. You can support the death sentence and that innocents should be defended. To say otherwise is to create a false dilemma (do you want me to define it for you or can you take responsibility and google it yourself?).

4. The limits are covered in the first two points so no the execution of an death row inmate does not exceed any limits.