They axed her when they realised she was too smart and wasn't asking the Doctor enough questions.
Tragically, Dr. Elizabeth Shaw had to leave UNIT when she was assigned to take part in the Prometheus expedition to discover the roots of mankind. There, she was impregnated with an alien fetus by an android, and then went on further adventures with the android's head.
Life Story Edit
So you wanna know about Liz Shaw, huh? Alright.
Bring the beat boys.
So I was a woman in UNIT in front of the Brig
cause I was already cool, but wanted to go big
he told me they dealt with weird crap from outer space
At first I couldn't believe he could keep a straight face
Then he introduced me to a cat with a two hearts
and, let me tell ya, he had all the smarts
Doc tried to leave with his blue TARDIS
But he couldn't, and he took it as a diss
Next thing I knew, it was gettin' crazy
Dolls was waking up, and man's fate was lookin' kinda hazy
But danger and death ain't never ever fazed me
So the Doc and me turned 'em back to plastic babies
And then we fought old lizards, alien astronauts, and evil Brig too
Damn, I can't even remember all the crap we've been through
But one day, I just had to go
The reason? Only my homie the Doc will ever know