To harvest root vegetable crops, you can use the Root Digger attachment (also known as the Potato Digger).
The round tines that extend from the back of the Root Digger sift through previously-worked soil, pushing your potatoes or other root crop toward the soil surface, so that you can harvest them. Typically, after using the Root Digger, your potatoes will be at least partially exposed.
The Root Digger can burrow as deeply as you have previously worked the soil, but it cannot burrow deeper than that. In other words, it is used for harvesting, not for plowing.
To use the Root Digger, you will need the Adjustable Tool Carrier and Wheel Weights. If you use wide rows, you may also want to use the Wheel Extensions so that you can better straddle the rows. Use of the Straight Bar Tool Carrier will enable you to use two Root Diggers in parallel.