I would say only to the extent that the Roman Catholic Church
neither approves nor disapproves of capital punishment, as
confirmed in the recent catechism, though there are many RCs
who were rather surprised and upset that capital punishment was
not explicitly condemned.

For myself, as a Catholic, I see my own opposition to capital
punishment as much the same as my opposition to abortion - a
reverence for life. Here in the UK, the anti-abortion case is
often let down by the explicit link which those on the
political left make with anti-abortionists and
pro-executionists. There is a tendency to condemn people who
hold both views as hypocrites. I feel that if there were many
more anti-abortionists who were also vocal in their opposition
to capital punishment on a pro-life line, it would end this
kneejerk association of anti-abortion as a right-wing thing,
and get many to think seriously about the issue (there are
plenty who are pro-abortion equally for a kneejerk left-wing
reason).

I do not think your biblical quote can automatically be taken
as support for capital punishment. I take it that as a Roman
Catholic you are opposed to abortion, and would still onsider
it wrong, and something to be objected to even if legalised by
"authority".