Shulchan Arukh Yoreh De'ah · Siman 10

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Seif 1 A new knife belonging to one who worships idols, or an old knife that has no question of being under the impurity of idolatry (or non-kosher use), it is permitted to slaughter a healthy animal with it because by doing so it it will cause a financial loss. However it is forbidden to slaughter an animal that will die anyway due to illness, because this is a positive financial gain (since otherwise, the animal would be lost). The knife (one acquired) belonged to an idolater that was sharpened on a kosher grinding wheel, or if there wasn't a defect on it one must stab it in the hard ground ten times, then one can slaughter permissibly. If someone slaughters with a non-kosher knife, one must wash the area of the neck where the slaughtering cut, and if one cuts away the meat from the area, it is praiseworthy.

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Seif 2 A knife that slaughters in a kosher manner, even though it is dirty with blood is permissible to slaughter again with it. However it is forbidden to cut something hot with it.And it is permissible to cut something cold with it if you rinsed off the blood first.

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Seif 3 A knife that slaughtered a trefa, it is forbidden to slaughter with it until it is washed with cold or it is wiped with something hard. The modern custom is to wipe the knife thoroughly on the animal's hair between each slaughtering, and this is proper to do, and if someone slaughters without washing it, we wash off the area of the neck where the slaughter cut. If one finds that he is regularly slaughtering many trefot, we need to stick the knife in hard ground ten times.