The Shulhan Aruch (Orah Haim 180:5) writes that it is customary to cover the knives on the table before reciting Birkat Ha’mazon. The Mishna Berura (Rav Yisrael Meir Kagan of Radin, 1839-1933) brings two reasons for this practice. First, since a knife is something which could be used to end a person’s life, it should not be exposed on the table, which resembles an altar – something that serves to prolong human life. The second reason, cited in the name of Rabbenu Simha, is that a certain person once became so distraught when reciting, "U’bneh Yerushalayim" – the section of Birkat Ha’mazon in which we pray for the rebuilding of Jerusalem – that he took a knife from the table and thrust it into his stomach. In order to ensure this does not happen, we should cover the knives on the table for Birkat Ha’mazon.
The Shulhan Aruch adds that it is customary to leave the knives uncovered for Birkat Ha’mazon on Shabbat and Yom Tob. Some explain that the festive aura of Shabbat and Yom Tob makes it highly unlikely that somebody would feel very distraught over the destruction of Jerusalem, and so there is no need to cover the knives. Other suggest that the observance of Shabbat and Yom Tob has the effect of "Mituk Ha’din" – "sweetening" the harsh judgments, and so it does not concern us that knives shorten human life. Another explanation is that the primary concern regarding knives involves using them when building the altar, and since building is forbidden on Shabbat and Yom Tob, knives may be left exposed on the table on these occasions.
In any event, the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909), in Parashat Hukat (6), writes based on the Arizal (Rav Yishak Luria of Safed, 1534-1572) that one should actually remove the knives from the table before Birkat Ha’mazon, and not just cover them. Moreover, the Ben Ish Hai writes that they should be removed even on Shabbat and Yom Tob, in contradistinction to the practice mentioned by the Shulhan Aruch. Therefore, it is proper to remove the knives from the table before Birkat Ha’mazon, even on Shabbat and Yom Tob.
Summary: It is customary to remove the knives from the table before Birkat Ha’mazon, both on weekdays and on Shabbat and Yom Tob.