This employee may just need to talk through their concerns and get your help prioritizing or delegating. They may, for example, feel like every single thing on their to-do list is life-or-death by Friday at close of business, when that’s not really the case.
Some manager guidance can go a long way, especially for your employees who are usually self-directed.
On the other hand, the stress and mental health effects the employee describes may rise to the level of a disability under the Americans with Disabilities Act (ADA). In this case, we would recommend beginning the interactive process to determine what, if anything, can be done to accommodate them so that the essential functions of the job get done to your standards and the employee is able to keep working. As part of this conversation, you can request a doctor’s note to substantiate the disability.
If you have more general concerns about the effects of stress in your workplace, you might consider ways to help your employees reduce and manage their stress. Tried and true methods include offering health benefits so employees can access health care professionals and paid time off so they can take a day here and there to rest and recharge. Simply encouraging employees to support one another and allowing them breaks during the day can also be a great help.