Glasset smutter ud af min hånd, hvis det er vådt.

Because glasset is the definite form of et glas.

• et glas = a glass
• glasset = the glass

In Danish, the definite article is usually added to the end of the noun as a suffix:

• en bil → bilen
• et hus → huset
• et glas → glasset

So here the speaker is talking about a specific glass: the glass.

Smutter is the present tense of smutte.

In this sentence, it means something like:

• slips
• slips out
• accidentally gets away

So Glasset smutter ud af min hånd means the glass slips out of the speaker’s hand.

It sounds a bit more like an accidental, sudden movement than a simple neutral verb like falder (falls).

Ud af is a very common combination meaning out of.

So:

• ud = out
• af = of / from
• ud af min hånd = out of my hand

In English, we also say slip out of my hand, so this matches quite well.

Even though a hand is not literally a container, Danish still naturally uses ud af in this kind of situation.

Because Danish normally uses the possessive directly before the noun:

• min hånd = my hand
• din hånd = your hand
• hans hånd = his hand

You do not normally combine a possessive like min with the ordinary definite ending:

• min hånd = correct
• min hånden = incorrect

So the possessive replaces the usual definite article idea.

Det refers to glasset.

That is important because:

• et glas is a neuter noun
• neuter nouns are referred to with det

So:

• glasset ... hvis det er vådt = the glass ... if it is wet

It does not refer to hånd, because en hånd is a common-gender noun, and that would normally be referred to with den, not det.

Because the adjective has to agree with a neuter noun or pronoun.

Here, det refers to glasset, and glas is neuter:

• et glas
• therefore: det er vådt

Compare:

• en bil er våd
• et glas er vådt
• de er våde

So the -t ending shows neuter singular agreement.

Danish often uses the present tense for:

• general truths
• repeated situations
• conditions
• things that happen whenever something else is true

So Glasset smutter ud af min hånd, hvis det er vådt means something like:

• The glass slips out of my hand if it is wet
• or in natural English, sometimes will slip out of my hand if it is wet

This is very similar to English, where we also often use the present tense after if in general statements.

Hvis means if and introduces a condition.

So here the meaning is: under that condition, the glass slips.

• hvis = if
• når = when

A rough difference is:

• hvis = conditional, not necessarily certain
• når = when, something expected or recurring

So hvis det er vådt is the normal choice for if it is wet.

The sentence has:

1. a main clause: Glasset smutter ud af min hånd
2. a subordinate clause: hvis det er vådt

In the subordinate clause, Danish does not use main-clause word order. That is why you get:

• hvis det er vådt
• not hvis er det vådt

So the order is:

• hvis
  • subject + verb + adjective

This is normal Danish subordinate-clause word order.

Yes. You can say:

Hvis det er vådt, smutter glasset ud af min hånd.

That is also correct.

When the subordinate clause comes first, the main clause still follows normal Danish main-clause rules, so the verb comes before the subject:

• Hvis det er vådt, smutter glasset ud af min hånd.

Not:

• Hvis det er vådt, glasset smutter ud af min hånd.

The comma is acceptable and very common, especially in teaching materials.

You may also see Danish written without that comma, depending on comma style. So both can occur:

• Glasset smutter ud af min hånd, hvis det er vådt.
• Glasset smutter ud af min hånd hvis det er vådt.

The version with the comma makes the clause boundary especially clear for learners.

Grammatically, no: det points to glasset.

That is because:

• glas is neuter → det
• hånd is common gender → den

So if the sentence were referring to the hand, you would expect den, not det.

That makes Danish clearer than English here, because English it could be more ambiguous.