I have no personal experience with the 600 Grizzly but it sounds like your shifter linkage mite need some adjustments.
Here's threads on the subject.
http://www.grizzlycentral.com/forum...-shifting-hi-low-problem-2001-griz-600-a.html
http://www.grizzlycentral.com/forum...000-600-grizzly-won-t-shift-into-reverse.html
Here's the parts involved
https://www.yamahapartspitstop.com/oemparts/a/yam/50038cc0f870021f60a0b727/shift-shaft
Here's threads on the subject.
http://www.grizzlycentral.com/forum...-shifting-hi-low-problem-2001-griz-600-a.html
http://www.grizzlycentral.com/forum...000-600-grizzly-won-t-shift-into-reverse.html
Here's the parts involved
https://www.yamahapartspitstop.com/oemparts/a/yam/50038cc0f870021f60a0b727/shift-shaft