Usually we're super-strict about keeping the speaker of a poem separate from the author of a poem. After all, poets often create fictional personas who they imagine to be speaking their work – not everything they write down is what they personally believe. But the line between the real-life Sylvia Plath and the speaker of "Daddy" is blurry. Plath's poetry is usually considered to be part of the Confessional movement, and "Daddy" certainly reads like a personal confession. Plath's father was a German immigrant, like the father in the poem. He died when she was young (eight years old), though not quite the same age as in the poem (ten years old). Plath, similar to the speaker in the poem, tried to commit suicide. Plath was married to her husband for about seven years when she wrote this poem, and the speaker's husband sucked her blood for seven years.
Despite these similarities, the speaker in this poem is different from Plath, as the characters of the speaker's father and husband are different from Plath's own father and husband. She has made herself, and them, into characters. Common sense and fact tell us that Plath's father was not really a Nazi, and her husband was not a vampire.
We can guess how Plath may have felt about her husband and father, but we shouldn't take anything about her relationships with these two men as fact from this poem. Sure, this poem may reflect how Plath felt at the moment she was writing this poem, but it would be unfair to make generalized conclusions about her relationships from it. One of the main benefits of writing poetry rather than, say, a memoir, is that it doesn't have to be non-fiction. You can stretch the truth in poetry, as Plath does in this poem.
The speaker is a persona that Plath created so that she could write a poem that may be based on her life, but isn't trapped by having to stick to the literal truth. Besides, if this poem were simply autobiographical, we'd miss out on all the other cool meanings that it could have – like "Daddy" being a metaphor for men in general, or a symbol of evil in the world.
So, now that we know the speaker is different from Plath, well, who exactly is she? She's a tortured woman, who lost her father when she was so young that he seemed huge and powerful, like God. Memories of him have caused her pain – they've made her want to die. When dying doesn't work, the speaker tries to find a husband just like her father. Her playful rhythm and rhyme juxtapose with the desperation and violence of her language, to make her words poisonous to these two men and their power over her. This poem is like a stake in the heart of her disturbing memories – by the end of the poem, she has killed them.