wanton / frivolous
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wanton
With the deliberate intention of causing damage or destroying something, without a reasonable cause or out of pure destructiveness.
Unbekannte haben die Parkbänke mutwillig zerstört.
Unknown individuals wantonly destroyed the park benches.
The word is made up of 'Mut' and 'Wille'. Here, 'Mut' does not mean 'courage', but comes from an older meaning referring to 'attitude' or 'intention'. So 'mutwillig' describes an action that happens out of sheer intention, without external pressure.
Er hat die Tür nicht aus Versehen, sondern mutwillig beschädigt.
He did not damage the door by accident, but deliberately.
'Mutwillig' can stand as an adjective before a noun or, as an adverb, describe an action more closely. As an adverb, it usually stands directly with the verb.
Das war eine mutwillige Zerstörung von öffentlichem Eigentum.
That was a wanton destruction of public property.
In the meaning 'intentionally destructive', 'mutwillig' is very often combined with verbs that describe a negative action. Typical phrases are 'mutwillig zerstören' (to wantonly destroy), 'mutwillig beschädigen' (to wantonly damage), or 'mutwillig anzünden' (to deliberately set on fire).
Die Feuerwehr geht davon aus, dass das Auto mutwillig angezündet wurde.
The fire department assumes that the car was deliberately set on fire.
When you read 'mutwillig' in connection with words like 'Klage' (lawsuit), 'Antrag' (application/motion), or 'Gericht' (court), it means 'without sufficient reason' or 'frivolous'. This is a typical use in legal and administrative language.
Der Antrag wurde abgelehnt, da er als mutwillig eingestuft wurde.
The application was rejected because it was classified as frivolous.
deliberately
'absichtlich' and 'mutwillig' both describe something that does not happen by chance. The important difference is in the evaluation. 'absichtlich' only says that someone does something deliberately. That can be good, neutral, or bad. 'mutwillig' almost always sounds negative: someone acts without a good reason, recklessly, or even with the aim of causing damage. Sometimes it can also describe exuberant, thoughtless behavior. Learners may confuse the words because both refer to a deliberate action. If you only want to say that something was intentional, use 'absichtlich'. If damage, destruction, or bad behavior without a reason is meant, 'mutwillig' fits.
Unbekannte haben in der Nacht mehrere Fensterscheiben mutwillig zerstört.
Unknown individuals deliberately destroyed several windowpanes during the night.
Zur Sicherheit schaltet der Lehrer das Gerät absichtlich erst nach der Erklärung ein.
For safety reasons, the teacher deliberately turns on the device only after the explanation.