The short answer is no. A few go karts do sit higher off the floor than others, and some have light suspension, and even roll cages – however, they can still only cope with the slightly rough terrain. Go karts are primarily designed for use on the road, because of this – many are simply not designed for off road use.
If you can find a go kart that is quite high from the ground and has suspension along with a roll cage, then yes – you can take it off the road. However, a dune buggy would be much more suitable. Dune buggies have larger engines and much better suspension along with sturdy, steel roll cages. This makes them ideally suited for off road use.
Go karts, however, aren’t useless away from the asphalt. They can be used on hard mud tracks perfectly fine, just keep an eye out for any obstacles such as logs and sticks, as even a simple stick can cause issues when driving a go kart, due to the fact that they are so low to the ground.
If you want to take your go kart off the road, as well as keep it on the road; then you’re in luck. With a few modifications, you can be off road ready easily! Simply swap out the wheels for off road wheels, if this is possible with your go kart, and add some suspension. If you know a competent mechanic or are comfortable with welding, then you should be able to do this with no problem. This will raise the go kart significantly, and the off road wheels will give you much more traction. If you prefer to be safer, then you can even add a simple roll cage as well. However, the easier option is to just buy a dune buggy if you want to go off the road.