Explain why the burning of wood and cutting it into small pieces are considered as two different types of changes.

Burning of wood $-$ chemical change because a new substance is formed.

            $wood+O_2⟶Ashes+{CO}_2+△+light$

                                                                     (heat)

Whereas cutting into small pieces is a physical change because there is no change in the composition of the substance and no new substance is formed.

Only the size is reduced.