Beast is one of my favorite heros because he is a great farm and fun to play.
I like to play mid with him because at lvl 6 u just have to ult, attack a bit and use axes, and he will probably die unless pudge is their midder.
Beast is a great farmer because his attacks are quick and when u got quelling blade u farm very well.
Mid lane play
Just go for the last hit. Never waste mana until u get lvl 6, unless u are sure that u will kill him. U must be able to farm well enough to buy a ring of health at lvl 4/5.
When u are lvl 6 u use ult when has like 3/4 or 1/2 of life and u will certainly kill with axes. Lvl 7 gank or keep farming mid. Ult and axes u kill a squishy hero and u will be so fed that u will probably win game
Ult in a way that will slow all, but use on their carry so he wont do nothing in that team fights and will let ur team win the battle. Use axes all time to take some life.