kono houtyou ha yoku kireru node, ninzin wo tiisaku kiru toki ni benri desu.

Yes—here 切れる is the same form as the potential of 切る, and with a tool like 包丁 it often means can cut well or simply is sharp / cuts well.

So:

• 切る = to cut
• 切れる = can cut / cuts well

In this sentence, この包丁はよく切れる does not mainly mean this knife is able to cut in the basic sense. A knife is obviously for cutting. Instead, it means the knife cuts efficiently or sharply.

So a natural interpretation is:

• This knife cuts well
• This knife is nice and sharp

One thing that can confuse learners is that 切れる can also be an independent intransitive verb in other contexts, but here the meaning is clearly cuts well.

Here, よく means well, not often.

That is a very common point of confusion because よく can mean both:

• often
• well

Examples:

• よく日本語を勉強します = I often study Japanese.
• よく見える = can see well
• よく切れる = cuts well

In this sentence, because it is describing the performance of a knife, well makes sense:

• この包丁はよく切れる = This knife cuts well.

If you tried to read it as often cuts, that would sound strange.

Because 小さい is an i-adjective, and when an i-adjective modifies a verb, it changes to its -く form.

So:

• 小さい = small
• 小さく = in a small way / into small pieces

In にんじんを小さく切る, 小さく describes how the carrots are cut.

So it means:

• cut the carrots small
• more natural English: cut the carrots into small pieces

This is the same pattern as:

• 早い → 早く
  早く食べる = eat quickly
• 細かい → 細かく
  細かく切る = cut finely

This part means when cutting carrots into small pieces.

Breakdown:

• にんじんを = carrots (direct object)
• 小さく切る = cut into small pieces
• とき = time / when
• に = at / in

So:

• にんじんを小さく切るときに = at the time of cutting carrots small
• natural English: when cutting carrots into small pieces

The clause before とき works like a modifier of とき:

• [にんじんを小さく切る] とき
• the time when one cuts carrots into small pieces

This is a very common Japanese structure.

The に after とき marks the time point or situation: at the time when...

So:

• 切るとき = when cutting
• 切るときに = when cutting / at the time of cutting

In many cases, the に is optional, and both versions sound natural. The difference is usually small.

• にんじんを小さく切るとき便利です
• にんじんを小さく切るときに便利です

Both can work, but ときに can sound a little more explicitly tied to the situation when doing X.

So learners should think of this as a normal and common pattern, not something mysterious.

Both ので and から can mean because / so, but they have different nuance.

• から often sounds more direct and assertive.
• ので often sounds softer, more explanatory, and a little more objective.

So:

• よく切れるので、便利です
• Because it cuts well, it is convenient

This sounds smooth and natural because the speaker is calmly giving a reason.

If you used から:

• よく切れるから、便利です

that would also be grammatical, but it can sound a little more straightforward or conversational.

A simple rule of thumb:

• ので = softer explanation
• から = more direct reason

は marks 包丁 as the topic of the sentence.

• この包丁は = as for this knife...

The sentence is basically making a comment about this knife:

• This knife cuts well, so it is convenient...

Using は makes sense because the knife is the main thing being talked about.

If you used が instead, the nuance would change. が would focus more on identifying this knife as the thing with that property, while は sounds more like speaking of this knife...

For learners, the simplest understanding here is:

• この包丁は = this knife is the topic of the sentence

Because にんじん is the direct object of 切る.

In the part:

• にんじんを小さく切る

the thing being cut is the carrot, so it takes を.

That is true even though the whole sentence is about the knife. Inside the when cutting carrots clause, にんじん is still the object of cut.

So:

• 包丁は = topic
• にんじんを = object of 切る

Different parts of the sentence can have different grammatical roles.

In this sentence, 便利です is describing this knife.

The topic at the start is:

• この包丁は

So the sentence is saying:

• This knife cuts well, so it is convenient when cutting carrots into small pieces.

In other words, the knife is handy for that situation.

Japanese often leaves repeated subjects unstated, so after introducing この包丁は, the sentence continues describing that same topic unless something clearly changes it.

So the meaning is not:

• Cutting carrots is convenient

but rather:

• This knife is convenient to use when cutting carrots small

It may look repetitive in English, but in Japanese it is completely natural.

They are doing different jobs:

• よく切れる = the knife cuts well / is sharp
• にんじんを小さく切る = to cut carrots into small pieces

So one describes the quality of the knife, and the other describes the action you do with it.

Japanese often repeats the same verb root when the meaning is still clear and natural. This is not usually considered bad style in simple everyday sentences.

In fact, avoiding the repetition too hard can make a sentence sound less natural than just saying it directly.

Yes. 便利 can be translated in several ways depending on context:

• convenient
• useful
• handy

In this sentence, all of these are possible:

• This knife is convenient when cutting carrots into small pieces.
• This knife is useful for cutting carrots into small pieces.
• This knife is handy when cutting carrots into small pieces.

Handy is often especially natural in English for tools.

So while 便利 is often taught as convenient, the best natural translation here may actually be handy or useful.

Before とき, Japanese usually uses the plain form of the verb.

Here:

• にんじんを小さく切るとき

means when cutting carrots into small pieces.

The plain non-past form is normal here because it refers to the action as a general situation or repeated occasion, not one specific past event.

Compare:

• 日本へ行くとき = when going to Japan
• 食べるとき = when eating
• 寝るとき = when going to bed / when sleeping

So 切るとき is just the standard grammar pattern for when cutting.