The shulchan aruch codifies that a Kohen who kills someone may not bless the people. If, in the times when the Sanhedrin administered capital punishment, a Kohen saw a situation that warranted the death punishment by stoning, and the person was convicted, and the kohen as a witness participated in the stoning, would he be disqualified from blessing the people?
R. Ephraim Bilitzer (Yad Ephraim no. 5), in addressing the question how could Phineas perform the priestly service after killing Zimri & Kosbi, admits as obvious that only a kohen who was not performing a commandment by killing another is subject to disqualification - not a kohen who was performing a commandment, as Phineas was (cf. Rema CM 425:4). In the case of capital punishment too, once it is determined by the sanhedrin that the accused is guilty his execution is a biblical commandment (see Rambam, Laws of Sanhedrin 14:2-3). In solidifying his view, R. Bilitzer cites from Chizkuni (Num. 25:12) that Phineas was worried he may lose his priestly status if he were to kill Zimri and Kosbi as the law dictates, and so God had to assure him that since the killing is for the sake of heaven he can still maintain his priestly status.
Rav Ovadia Yosef in Yechaveh Daat (2:14) was asked about whether a Kohen who fought in the IDF and during the battle killed a terrorist is permitted to perform the blessings.
Rav Ovadia after discussing the issue at length concludes that it is permitted. For the killing of this terrorist was a mitzvah.
With this in mind, it would be permitted for the kohen to continue to bless the people, even after he took part in the stoning, as carrying out the punishment of stoning is a mitzvah.
The Gemoro Brochos 32b says no a Cohen who killed shouldn't do bircas cohanim
ברכות דף לב: כהן שהרג נפש לא ישא את כפיו שנאמר ידיכם דמים
Tosfos in Yevamos 7a "sheneemar"says either because of a chumra or because the hands which killed as accusants cannot become defendants:
לא ישא את כפיו חומרא בעלמא הוא ועוד דוקא לא ישא את כפיו לפי שהרגו בידו ואין קטיגור נעשה סניגור וכדכתיב בההוא קרא ובפרישכם כפיכם: -
He should only refrain from blessing by raising his hands because he killed with the very same hands and an accusant cannot become a defendant.
Note that Tosfos says there that with regards to Avoda i.e serving in the Beis Hamikdosh there is no such prohibition hence thats why Pinchos was able to become Cohen Gadol after killing Zimri. But it could be he never performed Bircat Cohanim ever again and let the other Cohanim bless the people. See Shevet Halevi (thanks to Jay) who quotes Tosfos as Halacha