Question:
Wrists bound,
I am slave to all I want.
Feet bound,
I am slave to all my wrongs.
Hands tied,
I am slave to my desire.
My heart cries,
I am a slave to my fear.
Demand purity, and
Still I bring You dirt.
Soiled and stubborn,
Pierce my beating heart.
Speak a word,
Break my dying mind.
Pull me close,
Place a purpose on my life.

I need Your hope, I need Your wings
To fly.
Answer:
Originally Posted by SarahTheGuitarist Wrists bound,
I am slave to all I want.
Feet bound,
I am slave to all my wrongs.
It's a fine opening, but it doesn't have much 'hook' to it. It's not original enough to make someone sit up and take notice, unless the music does it.
Hands tied,
I am slave to my desire.
My heart cries,
I am a slave to my fear. The rhymes here make me think that perhaps you ought to change the 'bound' repetition in the first verse.
I like the "My heart cries" "slave to fear" lines.
Demand purity, and
Still I bring You dirt.
Soiled and stubborn,
Pierce my beating heart.
Speak a word,
Break my dying mind.
Pull me close,
Place a purpose on my life. A few things here--I like the first two lines especially, but 'break my dying mind' seems almost redundant, your contrast doesn't make any difference-the mind goes from dying to broken.

I need Your hope, I need Your wings
To fly. I like it--it's got a nicely polished and snugly fit feel, but it's a bit cliche. You'll need to back this song up with interesting music to make it work.