If you’re struggling with board clears, perhaps it’s because you’re trading minions too much. Remember that the win condition for this deck is to gain tempo over your opponent with your upgraded hero power and not trade too much with your minions. Even if the favorable trades look good, midrange and control decks will still out value you, namely board clears in your case.
So I guess my advice is to play faster. Clear board threats using your dagger, SI:7 Agent combo power, Deadly Poison, Southsea Deckhands, and maybe Cold Blood whenever possible. Otherwise, just remember that you’re playing an aggro deck—sometimes it’s okay to just ignore your opponent’s threats to make yours bigger. Even if your board gets cleared, you should be able to finish your opponent using the aforementioned cards by that time. Otherwise, tough luck.