jemandem etwas zufügen
to inflict
To cause someone something negative, such as pain, damage, suffering, or an injury.
Der Täter hat dem Opfer erhebliche Verletzungen zugefügt.
The perpetrator inflicted serious injuries on the victim.

to inflict / to add
Loading your saved state.
to inflict
To cause someone something negative, such as pain, damage, suffering, or an injury.
Der Täter hat dem Opfer erhebliche Verletzungen zugefügt.
The perpetrator inflicted serious injuries on the victim.

'Zufügen' (to inflict / to add) is a separable verb. The prefix 'zu' is separated from the verb in a main clause and placed at the end of the sentence. In subordinate clauses or in the infinitive, the verb stays together.
Er fügte dem Gericht noch etwas Pfeffer zu.
He added a little more pepper to the dish.
This verb almost always requires two objects. The person or thing to which something is added or done is in the dative. What is added or inflicted is in the accusative. The structure is: jemandem (dative) etwas (accusative) zufügen.
Der Sturm hat dem Haus (Dativ) großen Schaden (Akkusativ) zugefügt.
The storm inflicted great damage (accusative) on the house (dative).
In the meaning of 'etwas Negatives verursachen' (to cause something negative), 'zufügen' is always combined with negative nouns. Common collocations are 'Schaden zufügen' (to cause damage), 'Schmerzen zufügen' (to cause pain), 'Leid zufügen' (to cause suffering), or 'eine Niederlage zufügen' (to inflict a defeat).
Pass auf, dass du dir selbst keine Verletzung zufügst.
Be careful that you don't inflict an injury on yourself.
In the meaning of 'hinzufügen' (to add), the verb is very often used in recipes or cooking instructions. Here the objects are neutral things such as ingredients, spices, or liquids.
Fügen Sie der Suppe eine Prise Muskatnuss zu.
Add a pinch of nutmeg to the soup.
to remove
'entfernen' and 'zufügen' are opposites when it comes to an existing amount or mixture. 'entfernen' means that you take something away. Here, 'zufügen' means that you add something to it. The difference is especially clear with recipes or mixtures: you do not remove an ingredient from the bowl again, but you add a new ingredient.

Mein Freund fügt der Suppe noch etwas Salz zu.
My friend adds a little more salt to the soup.
Omar entfernt die Kerne, bevor er die Paprika schneidet.
Omar removes the seeds before he cuts the bell pepper.