Wir trennen den Saum auf.

Because the verb here is a separable verb: auftrennen.

In a normal main clause, German splits separable verbs into two parts:

• the conjugated base verb goes in the usual verb position
• the prefix goes to the end

So:

• Wir trennen den Saum auf. = We unpick/open the hem.

But in the infinitive, the parts stay together:

• den Saum auftrennen

This is a very common German pattern, like:

• Ich stehe auf. → infinitive: aufstehen
• Wir machen die Tür auf. → infinitive: aufmachen

The full dictionary form is auftrennen.

• trennen by itself usually means to separate
• auftrennen means something more like to unpick, unstitch, rip open along stitches, depending on context

In sewing, auftrennen is the natural verb for undoing a seam or hem.

So in this sentence, trennen ... auf is not just trennen plus a random auf. It is one verb: auftrennen.

Because Saum is the direct object of the verb, so it is in the accusative case.

Saum is masculine:

• nominative: der Saum
• accusative: den Saum

So:

• der Saum = the hem, when it is the subject
• den Saum = the hem, when something is being done to it

Here, we are doing the action, so wir is the subject, and den Saum is the object.

Saum usually means hem in clothing or fabric.

It can refer to the finished edge of a piece of cloth, especially one that has been folded and sewn.

In other contexts, Saum can also mean an edge or border, but in a sewing sentence, hem is the most likely meaning.

German main clauses usually place the conjugated verb in second position.

So the structure here is:

• Wir = subject
• trennen = conjugated verb, in second position
• den Saum = object
• auf = separated prefix at the end

That gives:

• Wir trennen den Saum auf.

This is the normal word order for a separable verb in a main clause.

It is present tense.

The verb auftrennen is being conjugated for wir:

• ich trenne auf
• du trennst auf
• er/sie/es trennt auf
• wir trennen auf
• ihr trennt auf
• sie/Sie trennen auf

So Wir trennen den Saum auf literally means We unpick the hem or We are unpicking the hem, depending on context.

German present tense often covers both English simple present and present progressive.

No, not in a normal main clause.

In a main clause, a separable verb must split:

• Wir trennen den Saum auf.

You keep it together only in certain forms, such as:

• infinitive: den Saum auftrennen
• with a modal: Wir müssen den Saum auftrennen.
• perfect participle: Wir haben den Saum aufgetrennt.

So Wir auftrennen den Saum is not standard German word order.

The infinitive is:

• auftrennen

So if you wanted to say to unpick the hem, you would say:

• den Saum auftrennen

That is the form you would normally look up in a dictionary.

They are related, but not the same.

• trennen = to separate, divide
• auftrennen = to undo by opening/unpicking, especially stitches or seams

Examples:

• Wir trennen die Gruppen. = We separate the groups.
• Wir trennen den Saum auf. = We unpick the hem.

So in sewing, auftrennen is much more specific and natural.

A common spoken past form would be the Perfekt:

• Wir haben den Saum aufgetrennt. = We unpicked the hem.

Notice what happens to the separable verb:

• infinitive: auftrennen
• past participle: aufgetrennt

The prefix auf- stays attached in the participle.

You could also see the simple past:

• Wir trennten den Saum auf.

But in everyday spoken German, haben ... aufgetrennt is usually more common.

It is especially common in sewing, tailoring, and similar contexts where stitches, seams, hems, or seams are being undone.

For example:

• eine Naht auftrennen = to unpick a seam
• den Saum auftrennen = to unpick the hem

In other contexts, it can sometimes mean opening or splitting something apart, but sewing is one of its most common uses.

A simple pronunciation guide:

• Wir sounds roughly like veer
• trennen sounds roughly like TREN-nen
• den sounds like dayn with a shorter vowel
• Saum rhymes roughly with English ow in cow, but with an s at the start

So the sentence sounds approximately like:

• Veer TREN-nen dayn zowm owf

That is only an approximation, but it can help as a starting point.