Yes, masticating juicers are more than capable of juicing tough vegetables like carrots and beets.
In fact, many would argue that masticating juicers are better than centrifugal juicers for juicing carrots.
The reason many people think this is because with a masticating juicer the process is slower, but as a result, a lot more of the nutritional value of the vegetable is retained in the juice.