Anything ranged and a slow ruins him. Viper is particularly awesome and although axe also counters dazzle's grave, dazzle's heal bomb wins the early game against him.
I should've just stopped at my first sentence. Literally any ranged hero with a slow allows you to kite him. You really want a carry that can clear the wave as well though. Personally I love playing meepo vs a cutting axe.
Actually, the best way to counter an Axe backdoor is to forget last hitting and to fight him. You may lose the fight, but he will need regen so you would have more farm by suiciding to an Axe while dealing much damage as you can than trying to withstand the backdoor.
http://www.dotabuff.com/matches/2411408324
MY AXE GOES TO TRANQUIL + RUSHING BM NO VANGUARD NO BLINK
off course he misses every calls
PRAY THE AXE IS RETARDED LIKE THIS ONE AND U GOOD ( DUAL OFFLANE AXE + ABADDON FAIL HOW THE FUCK WE MANAGED TO DO THAT)
range heroes/strong early sups/switch lanes
armor red also works sometimes but better try some of the above
Shit on his face 
I've beaten an Axe-Omni-Riki trilane hard today as wd
http://www.dotabuff.com/matches/2412760512
FeelsGoodMan
DAZZLE????? litterally the best lane counter to axe there is...' he's also an pseudo-anti-tank hero
When axe is cutting ur creepsx go to his creeps and lead them away from ur tower. Maybe into a jungle camp so u can farm the creeps possibly.
Supports in your lane must follow you so you dont feed if axe decided to go on you
If Ur In A Normal Match - Pick Axe Then Repick
If U Want To Play Ranked Play Captains Mode..
This Axe Was Really Troublesome With Io....
You pray that you don't have a jungle legion on your team, or else your lanes are gonna be too weak.
Будь ласка, увійдіть до системи для написання коментарів.
I'm just asking since there are so much matches with axe in it and they'd just cut off the creep wave at the opponents safelane.
is there any way I could've won these matches?
http://www.dotabuff.com/matches/2406370243
(tri lane with warlock and riki)
http://www.dotabuff.com/matches/2411352207
(duo with necro)
and any tips on how to counter them in my further matches?