Dazzle basically does have infinite mana because he has excellent INT and his spells have pretty low costs. His autoattack is hardly negligible, it starts at a pretty good level and continues to grow well due to his high INT growth. Once he finishes Medallion, Dazzle can hit quite hard with auto+touch, and will have sufficient regen (again, due to his high INT growth) to do it frequently.
Weave will also completely shut down TA's burst as well as make her more vulnerable. Oh, you pierce 8 armor with Meld? np, I'll just give my entire team +15 (on average) armor.
You're getting so hung up on farming. Who the fuck cares? As long as you don't lose your lane against TA, you're perfectly fine. She can't carry. And before those items, she's not even that strong of a ganker - sure as hell she isn't as good as QoP, Nightstalker, or many others. I mean, yeah, she could probably wander over and blow up a hard support, but that's another example of pros not really experimenting much - if that support gets a couple of cheap items (like maybe bracer+chainmail), TA can't turn him into giblets with two hits anymore.@PizzaSHARK Anything you say has no credibility because you shown over and over again how you lack understanding of the game. TA not good before Desolator/Dagger? If she wasn't, how would she even farm those items against any strong mid hero?
TA doesn't reach that "oh wow she just gibbed our fed hero in three hits," level until she gets both her blink (needed to actually catch people out, as well as get out of tight situations) and desolator (needed to give her the damage amp she requires to reach that kind of burst.) That's 6300 gold, on top of the bottle, the boots, and anything else she might need. It's not like it's game over because TA has 60 CS at 10 minutes, and you have to keep in mind that her ability to show up and blow up people - which is the reason most people think she's so good - isn't really there until she has those items. And, assuming you haven't been losing your lanes (don't necessarily have to win them, just can't lose them), by time she has those items your team should have some items of your own.
And as Lysah's been saying, there are several heroes you can pick that will counter the shit out of TA in mid. Counter her as in "get the fuck away from the creeps or I'll kill you."