Mary Shelley included the poem Mutability by Percy Bysshe Shelley (her husband) because the central theme of the poem is intrinsically connected with the fate of Victor Frankenstein. 

We rest; a dream has power to poison sleep.
We rise; one wand'ring thought pollutes the day.
We feel, conceive, or reason; laugh, or weep,
Embrace fond woe, or cast our cares away;
It is the same: for, be it joy or sorrow,
The path of its departure still is free
Man's yesterday may ne'er be like his morrow;
Nought may endure but mutability!

Mutability is the essence of life: It is the combination of all the elements and circumstances which directly affect our destinies and change our lives forever.  At first glance the poem does not seem to fit in the narrative at that specific point in the story. Yet, if we analyze the message of the poem, we realize that mutability has indeed been ever-present in the story.

From the very beginning we see that something big will happen to Victor and that it may not necessarily be something good. His hunger for learning, his obsession with the idea of creating life, and his intensity of character can help us predict that a huge change is in the horizon for him. Hence, mutability is the source of that change which not only affected Victor, but also Elizabeth, Henry, William, and Justine.