DestroyAPIView

views.py

class PersonDeleteView(DestroyAPIView):

    serializer_class= PersonSerializer
    queryset= Person.objects.all() #en vez de all se puede poner el filter

serializers.py

class PersonSerializer(serializers.ModelSerializer):
    class Meta:
        model=Person
        fields=(
            '__all__'
        )

urls.py

    path(
        'api/persona/delete/<pk>',
        views.PersonDeleteView.as_view(),
        name=''
    ),