Originally Posted by Taco John
For the same reason she didn't in the books. She's a young girl who is attacking people being mean to her, not being militarily strategic. It's a huge part of her character through the whole book. She does things without thinking through her actions and their consequences.
And that point is driven home much more clearly in the books than it is in the TV series. In the books we understand while it would have made far more sense for her to use one of her 'deaths' on Gregor Clegane, she instead uses it on one if his cronies who brags about his participation in the gang rape of a young bar maid. Martin is careful to only give her fleeting glimpses of Tywin and his banner men before they return to the field of battle.
The show has her constantly playing with a knife and wrestling with her own internal desire to take Tywin's life herself, haulted largely due to timing and her confidence in her ability to successfully complete the dead. So, it makes even less since that when provided the ultimate opportunity to accomplish the task, she doesn't once consider it.
Plus, Tywin's entire extended sojourn in Harenhaal doesn't entirely make sense while Rob is largely running unchecked through his own lands. In the book he immediately returns to the field of battle in Pursuit of Robb's hosts only to be turned back by Edmure Tully's forces long enough for him to hear of Stannis marshalling his own forces and attacking Kings Landing. Now, a lot of that obviously would need to be streamlined. But it would have made much more sense for Tywin to have been out and about with the writers throwing out occasional references to him hitting pockets of resistance instead of just sitting in Harenhaal exchanging witty banter with some peasant girl he randomly plucked out of a crowd of prisoners and apparently trusts to handle his food and drink. (yeah, huge logical problems with this act as well. Robert used Lancel Laninster as his Cup bearer and Tywin is willing to slum it with an unknown peasant girl?)
And why did we get this massive change? Because the show runners fell in love with the chemistry between Charles Dance and Maisie Williams. So, they let their love of a few scenes and clever dialog override story structure. That's a freshman film school mistake.