Once you reach level 15 you unlock your Medicinal Garden and you are able to grow, harvest and use Medicinal Plants for curing your patients and making more advanced cures in your Lab Makers.
To clear a Garden Field from an old plant you will need a shovel. Shovels are a special item you can randomly get rewarded with while collecting cures, curing patients, helping other players with renewing their Medicinal Garden fields while visiting their hospitals, in gift boxes or when opening the speech bubbles over the heads of your patients.
You can also get shovels in special bundles available available via the bundle section accessible by tapping the "!" button in the upper right of the screen.