Владислав

Предлагаю реализацию через интерфейс IHostingEnvironment. Вот примерный вариант решения.

…
using Microsoft.AspNetCore.Hosting;

public class HomeController : Controller {
        private ApplicationContext db;
        IHostingEnvironment _appEnv;

        public HomeController (ApplicationContext context, IHostingEnvironment appEnvironment) {
            _context = context;
            _appEnv = appEnvironment;
        }

        private bool RemoveFileFromServer (string path) {
            string fullPath = _appEnv.WebRootPath + path;
            if (!System.IO.File.Exists (fullPath)) return false;
            try {
                System.IO.File.Delete (fullPath);
                return true;
            } catch (Exception e) {
                //Debug.WriteLine(e.Message);
            }
            return false;
        }

        [HttpPost, ActionName("Delete")]
        [ValidateAntiForgeryToken]
        public async Task<IActionResult> DeleteConfirmed(int id)
        {
            var fileModel = await _context.Files.SingleOrDefaultAsync(m => m.Id == id);
            RemoveFileFromServer(fileModel.Path)
            _context.Files.Remove(fileModel);
            await _context.SaveChangesAsync();
            return RedirectToAction(nameof(Index));
        }
}