Después de respirar hondo, dejó de tartamudear y terminó la presentación con calma.

Because after después de, Spanish normally uses an infinitive when the subject is the same as in the main clause.

• Después de respirar hondo = After taking a deep breath
• Not después de respiró hondo, because respiró is a finite verb form, and that structure does not work here.

A similar pattern:

• Antes de salir, cerró la puerta. = Before leaving, he/she closed the door.

If the subject changes, Spanish usually uses a different structure:

• Después de que respiró hondo, comenzó a hablar.

Here, respirar hondo is a very common expression meaning to take a deep breath or to breathe deeply.

So:

• respirar hondo = the natural idiomatic expression

Although profundo means deep, Spanish usually says:

• respirar hondo rather than
• respirar profundo

A useful thing to remember is that Spanish often prefers certain fixed combinations, and this is one of them.

Dejar de + infinitive means to stop doing something.

So:

• dejó de tartamudear = he/she stopped stammering/stuttering

More examples:

• Dejó de fumar. = He/She stopped smoking.
• Dejaron de hablar. = They stopped talking.

This is a very common structure in Spanish, so it is worth learning as a chunk:

• dejar de + infinitive = to stop + -ing

Yes, tartamudear means to stutter or to stammer.

In British English, stammer is very common. In American English, stutter is more common.

So:

• dejó de tartamudear can be translated as either
  • he/she stopped stuttering
  • he/she stopped stammering

Also useful:

• tartamudo / tartamuda = a person who stutters or stammerer (depending on context)

They are in the preterite because the sentence describes completed actions in the past.

• dejó de tartamudear = he/she stopped stammering
• terminó la presentación = he/she finished the presentation

These are viewed as whole events with an endpoint.

Why not the imperfect?

• The imperfect would suggest an ongoing, habitual, or background action.
• Here, the speaker wants to present two finished actions in sequence.

So the preterite is the natural choice.

Because Spanish often leaves out subject pronouns when the verb ending already shows the person.

• dejó
• terminó

Both forms tell us it is he/she/you formal in the preterite.

Spanish is a pro-drop language, so subject pronouns are often omitted unless needed for:

• emphasis
• contrast
• clarification

For example:

• Después de respirar hondo, dejó de tartamudear... is perfectly natural.
• You would add él or ella only if you wanted to stress who it was.

Here it most naturally means finished the presentation.

• terminar algo = to finish something
• terminar la presentación = to finish the presentation

In some contexts, terminar can also be translated as end, but with a direct object like la presentación, finish is often the most natural English choice.

Compare:

• La presentación terminó. = The presentation ended.
• Ella terminó la presentación. = She finished the presentation.

Con calma means calmly, with calm, or in a calm manner.

So:

• terminó la presentación con calma = he/she finished the presentation calmly

Spanish often uses:

• con + noun where English might prefer an adverb.

Examples:

• con cuidado = carefully
• con paciencia = patiently
• con calma = calmly

So even though English often uses -ly adverbs, Spanish frequently uses this kind of phrase instead.

Grammatically, calmadamente exists, but con calma is much more natural and common in everyday Spanish.

So in this sentence:

• terminó la presentación con calma sounds natural
• terminó la presentación calmadamente sounds more unusual or formal

Spanish often prefers the simpler phrase:

• con calma

This is a good example of how the most literal adverb is not always the most natural choice.

The comma separates the introductory phrase from the main clause.

• Después de respirar hondo, = introductory time/action phrase
• dejó de tartamudear y terminó la presentación con calma. = main clause

In Spanish, a comma is commonly used after this kind of opening phrase, especially when it is a bit longer. It helps readability and makes the sentence clearer.

You may sometimes see short introductory phrases without a comma, but here the comma is very natural and standard.

Yes. Spanish allows some flexibility in word order, though some versions sound more natural than others.

For example:

• Después de respirar hondo, dejó de tartamudear y terminó la presentación con calma.
  This is the most neutral and natural version.

You could also say:

• Dejó de tartamudear y terminó la presentación con calma después de respirar hondo.

This is still correct, but the timing phrase now comes at the end, so the focus changes slightly.

Spanish word order is often flexible, but the original version is probably the best if you want to set the scene first: first the deep breath, then the rest.