The Shulhan Aruch (Siman 308) classifies a circumcision knife as Mukse "Machamat Hesron Kis"-because it is a valuable and delicate instrument, it will never be used for a purpose other than its intended function, out of fear that it will become damaged.
If there is a Mila on Shabbat, obviously, the knife may be handled to execute the Brit. The Poskim discuss at length what is the status of the knife after the Mila. Does it revert to being Mukse, and if so, what should the Mohel do with it upon completion of the Mila?
If the knife would still be in his hand, all agree that he could continue to hold it until it was properly stored. However, during the Mila, the Mohel puts down the knife immediately after cutting, so that he can perform the "Priah" with both hands. The question then becomes: Is he allowed to pick it up again and put it back in a safe place? There are four approaches in the Poskim.
1. The Bet Yosef cites Rabbenu Yerucham who seems to indicate that after the Mohel drops the knife, it reverts to its original Mukse status and may not be moved.
2. The Rama (YD 266) holds that since upon commencement of Shabbat, the knife was already designated to perform the Mila the next day, it has a purpose and does not become Mukse the entire Shabbat. Accordingly, after the Mila, the Mohel can still handle the knife. This is also the opinion of the Maharshal and the Shach.
3. The Elyah Rabbah and the Hatam Sofer (R. Moshe Sofer, Hungary, 1762-1839) suggest that the Mohel should hand the knife to a bystander, instead of discarding it on the table. He then becomes an accessory to the Misva and may handle the knife, just as the Mohel did. This is also the opinion of the Mishna Berura (Rav Yisrael Meir Kagan of Radin, 1839-1933) in Siman 310:16.
4. There is yet another opinion which suggests discarding the knife on a plate upon which there is already an item of value. The plate becomes a "Basis" (base) for both a permitted and forbidden item, which is permitted to be handled. The Mohel can then move the plate to a safe place.
Hacham Bension, as well as the Menuhat Ahaba agree with the last approach. However, Hacham Ovadia, in Halihot Olam, agreed with the position of the Rema, that the knife is not Mukse at all. Even though it is possible to rely on this lenient opinion, it is preferable to take into account Hacham Bension's position and use the plate as a base.
SUMMARY
As long as the Mohel is holding the knife, it is not Mukse. After he discards it, it is preferable to place it on a plate with another permitted item of value, and move the plate to proper storage. If that is not possible, Sepharadim may handle the knife regularly.