He actually doesn't have that many of the card itself in there. Destroy the first one as or just after it's laid down and you'll have a lot of breathing room. Also, it helps to use a deck that is in some way capable of destroying it. He won't put it at risk in a battle unless you trick or force him to.
I can wire anything directly into anything! I'm the Professor! - The Professor GT: xCOLBY JACKx
My strategy against it was like this 1. Ignore 1st creature, unless you have a lot of removal in your hand. I had some, but preferred to save it for later. 2. Remove Biovisionary as soon as it appears 3. All-out attack with whatever you have, if he only has 1/1 creature he probably won't block 4. Remove whatever creature got Followed Footsteps on 5. Attack until another Biovisionary appears, then kill it 6. If it copies one of your cards - depends on how annoying it is, but usually if he does it early in game they wouldn't be very powerful He has some breaks between casting Clones and Biovisionaries, so if you attack fast enough and get rid of multiple cloning cards it will be ok.
Chandra's deck is great against it if you get a few creature-killing spells in your hand. Basically decks with fast aggro and/or heavy removal should be fine.