Quick and dirty Harmony mod to completely disable the gamepad in Stardew Valley. Only tested on Windows.

ModEntry.cs

using Harmony;
using Microsoft.Xna.Framework;
using Microsoft.Xna.Framework.Input;
using StardewModdingAPI;
using StardewModdingAPI.Events;
using System;
using System.Reflection;

namespace SdvGamePad
{
    public class ModEntry : Mod
    {
        public override void Entry(IModHelper helper)
        {
            var harmony = HarmonyInstance.Create("com.vaindil.DisableSdvGamepad");
            harmony.PatchAll(Assembly.GetExecutingAssembly());

            InputEvents.ButtonPressed += (s, e) =>
            {
                if (e.Button == SButton.NumPad0)
                {
                    var state = GamePad.GetState(PlayerIndex.One);
                    Console.WriteLine("Gamepad connected? " + state.IsConnected);
                }
            };
        }
    }

    [HarmonyPatch(typeof(GamePadState))]
    [HarmonyPatch("IsConnected", PropertyMethod.Getter)]
    internal static class GamePadKiller
    {
        private static void Postfix(ref bool __result)
        {
            __result = false;
        }
    }
}