As mentioned, Grievous is adept enough to engage in hand-to-hand with Jedi. He almost wins his fight with Obi-Wan in episode 3, so he's got to have some incredible reflexes, but since he is too mechanical to be able to use the Force, he doesn't have enough warning to actually deflect a blaster bolt. Mythbusters tested the reaction time of a normal person to a Hollywood muzzle flash of a sniper, concluding that it was only just barely possible to dodge a bullet fired from a significant distance with an obvious muzzle flash.
That means that even with superhuman reflexes, there is no way Grievous could deflect a blaster bolt without knowing beforehand when it would be fired (I'm ignoring the segment Mythbusters also did on dodging Star Wars blaster bolts).
However, this doesn't mean that Grievous cannot deflect blaster bolts. This just means that he cannot do it intentionally and singly. If I were Grievous, constantly surrounded by blaster-wielding possibly hostile folk that it was kind of my job to irritate, I would figure out some way to protect myself from them. My line of thought would be, "If I can't block each bolt individually after it is fired, why don't I just block all possible shots when I'm in battle?" and that would lead me to think, "Hmm, rotatable wrists, four arms... why not reserve two arms for blaster defense?" And that's basically what Grievous does. He spins his sabers at a speed that makes it almost impossible to shoot through the sabers and actually hit him, meaning that he doesn't have to worry about being shot at because he already has his shield up.
The best evidence for this duality is Grievous's final scene. Clearly, nobody has shot Grievous yet, though it seems painfully obvious that someone, somewhere along the line, would have tried. Thus, Grievous can deflect blaster bolts when he has the use of all of his arms. When Grievous engages Obi-Wan, the first thing he does is spin two sabers (possibly just for the effect). When Grievous actually connects with Obi-Wan, he stops spinning the sabers because there is no longer a threat of blaster fire. When the clones attack and bolts start flying again, Grievous seems unconcerned because he believes his droids will handle the threat, meaning that he doesn't need to shield himself. When Obi-Wan finally kills Grievous, it is with a blaster shot, at almost point-blank range. Grievous, armed with an energy stick, cannot block the shot, proving that his reflexes are not fast enough to react to a single shot.
So yes and no. Yes, any lightsaber can be used to deflect blaster bolts if properly handled, and yes, Grievous can move his lightsaber fast enough to deflect blaster bolts, so yes, Grievous can physically deflect blaster fire. No, Grievous cannot use the Force, so no, Grievous cannot foretell a blaster shot, so no, Grievous cannot deflect individual bolts intentionally.