I have a 2001 Yamaha YZF 600R if I ride with out the Muffler could this cause damage?

No damage to the bike but you'll could possibly damage your ears! Why would you do this anyways? Sounds horrible and your asking for trouble...
 
yes over some time it would do it and really without a muffler you lose some power mostly lower end like take off i wouldnt run it with out
 
If you love your bike, don't do it. Removing the muffler all together falls into the same category of taking the packing out to make it louder. All that stuff is there for a reason - if you have to ask, leave it alone.
 
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