All nouns in Hebrew have a gender. Most are either male or female, but some have a dual-gender and can be referred to as either male or female. In this case, סכין is a noun than can be both male or female, and the example given uses it with a female form conjugation.
I hope this makes things clearer for you.
You want to know "why is that knife paired with a feminine verb?" - but your wording is awkward. In English a knife can't be a girl, but it can be seen as feminine (which means "girlish" but we don't say it that way.).
I'm glad Bezalel saw through that and was able to answer you.
I don't think it helps people who are new to the concept of grammatical gender to imply that an inanimate object itself can have gender. They need to be told clearly that it's only the noun that has gender. Otherwise, consider their confusion when they encounter the names of objects - and even body parts, such as רֶחֶם - that are associated with one biological gender more than another but do not have the same grammatical gender.
I think because the people inputting the correct answers didn't want to include too many weird syntactic orders. The most basic way of constructing that sentence is "The knife is cutting our food". While "the food of ours" is grammatically correct, it's clunky and not commonly used.