Translation:I cut the bread using a knife.
While I agree with the other commenters in that this sentence is a bit awkward and 「ナイフでパンを切りました」is the more natural way to say it, I think that the idea behind this question, and kind of with the use/write with a pen question, is to demonstrate that the て-form verb, in addition to connecting the two clauses, follows the tense of the verb at the end of the sentence.
In somewhat awkward English, this question can be written as "I used a knife, and cut the bread." 「つかって」becomes translated as "used" (past tense) because of 「切りました」(also past tense). To those who are used to thinking about Japanese verbs, this might sound super obvious, but て-form is often introduced as the verb form for requests and/or present continuous tense. That's just my guess as to what the course devs were thinking though ┐(ツ)┌
I also thought something like that.
I think this question in English would be something like "I cut the bread by using a knife" (some languages like Spanish don't need a word like "by" and allow you to put both sentences -and verbs- one after the other to express this, so I guess the analogy will be easier to make if you know any of them), and ナイフでパンを切りました would be "I cut the bread with a knife"
If you used the "using the knife" part at the end of the sentence I think it is wrong to use by. However, if the sentence is like
By using a knife, I cut the bread.
I think it's necessary. However, the emphasis would be on "using" -as in the original Japanese sentence (ナイフをつかって...). Can the two parts be changed in Japanese? I don't know how it could be done though.