why did tyrion sack janos slynt? was it because he double crossed eddard stark and he didn't want someone like that around or he has some private beef with him?

He didn't trust him after he betrayed Ned

But tyrion doesn't support stark either

Janoys Slynt was very much Cersei's man. Tyrion needed to place his own man in command of the gold cloaks in order to keep control as Hand. In the show he puts Bronn, in the book, some random guy whose name I forget, but is still more loyal to Tyrion.

It was Cersei's command to have Robert's bastards killed that really triggered him into realizing that he needs to seize the gold cloaks. (Although in the show, they changed it to Joffrey placing the command instead of Cersei, but the point of taking control is still valid.)

this