Here is how I would describe the "grinding" mentality. It means a willingness to play as many shots as needed, never missing, while refusing to make a single weak return, whether pushing, chopping, or counter-hitting, with a focus on returning anything that's not smashed or loop-killed, and relying on your reflexes to return some of those. It's primarily a defensive mindset, though grinders will often attack when given the chance. Some counter-hitters can play with this mindset and be pretty aggressive. Some fisher-lobbers styles play this way as well, with the underlying assumption that, to them, when fishing and lobbing they aren't making weak returns, since they are confident they can return the opponent's smashes as long as they keep their balls deep on the table.
How do you play against such a style? The keys are patience and decisiveness. If you play a grinder the same way you'd play an attacker, then you'll likely make too many mistakes, which means you are playing right into their game. Instead, you should take your time on your shots and focus on consistency until you get the right shot. After all, unlike when playing an attacker, you aren't fighting for the attack. But when the shot's there, you have to instantly change your mentality and end the point decisively. The difficulty in playing this style is finding that balance between consistency and decisiveness.
There are two great ways to learn to play against this type of mindset. The first is obvious - play against this type of player until you are comfortable. The other is to experiment with playing that way yourself, so you can see it from their point of view, and see how vulnerable they actually are, since they are basically letting the opponent dictate much of the play. Not only will you learn to play against that type of style, it'll improve your own consistency and ability to avoid weak returns, which will likely help your own game. So . . . happy grinding!