Se enfrió hasta el punto de que lo cortamos.

Because Spanish often uses the pronominal verb enfriarse to mean to get cold / to cool down.

• enfriar = to cool something
• enfriarse = to become cool / to get cold

So:

• Enfrié la sopa = I cooled the soup
• La sopa se enfrió = The soup cooled down

In your sentence, se enfrió shows that the subject underwent the change of temperature.

Not really. This is one of those cases where se is part of the verb rather than a truly reflexive idea.

A true reflexive verb would mean the subject does something to itself, like:

• Se lava = He washes himself

But se enfrió usually just means it got cold / it cooled down, not that it deliberately did something to itself.

Enfrió is the preterite, third person singular, of enfriarse / enfriar.

So it means that the cooling happened as a completed event in the past.

• se enfrió = it cooled down / it got cold

The preterite is used because the sentence presents this as a finished change that led to another finished action.

Because enfrió presents the change as a completed event: it reached that colder state.

• Se enfrió = it cooled down / got cold
• Se enfriaba = it was cooling down / used to cool down

In this sentence, the idea is that the cooling reached a point and then we cut it, so the preterite fits better.

The accent mark shows where the stress goes: en-fri-Ó.

Without the accent, Spanish spelling rules would make you stress it differently. So the written accent is needed in this verb form.

This is just the normal spelling of that past-tense form.

It is a fixed expression meaning something like to the point that or to such an extent that.

It introduces a result clause: the first part describes a degree or intensity, and the second part gives the consequence.

So the structure is:

• Se enfrió ... = it cooled down ...
• hasta el punto de que lo cortamos = ... to the point that we cut it

It is a fairly natural, slightly more formal or emphatic way to express result.

Because the full expression is hasta el punto de que.

Here, de belongs to the phrase el punto de, and que introduces the clause that follows.

So this is not an error or an optional extra word. It is just the normal structure of this expression.

A useful comparison:

• hasta el punto de que = to the point that
• hasta tal punto que = to such a point that

Notice that the second version does not use de.

Yes. Se enfrió tanto que lo cortamos is a very natural alternative.

Both sentences express result, but there is a slight difference in style:

• Se enfrió tanto que... = more straightforward, very common
• Se enfrió hasta el punto de que... = a bit more emphatic or formal

So the original sentence is correct, but it sounds a little more elaborate.

Lo is a direct object pronoun. It replaces a masculine singular noun, or sometimes a general it depending on context.

So lo cortamos means we cut it, where it refers to something already known from the conversation.

For example:

• el queso → lo
• el pan → lo

If the thing were feminine singular, you would normally use la instead.

Cortamos is preterite, so it presents the cutting as a completed action.

• lo cortamos = we cut it
• lo cortábamos = we were cutting it / we used to cut it

In this sentence, the cutting is a specific finished action that happened as a result of the cooling, so cortamos is the natural choice.

Because Spanish often leaves subject pronouns out when the verb form already makes the subject clear.

• se enfrió already tells you the subject is he/she/it or a singular noun
• cortamos already tells you the subject is we

So Spanish does not need to say ello or nosotros unless there is special emphasis or contrast.

For example:

• Nosotros lo cortamos = We cut it
• Lo cortamos = We cut it

Both are correct, but the second is more neutral and more common.