Please help! MTD Riding Mower Engine Troubleshooting

I have an older MTD riding mower with a Briggs & Stratton egine. She ("Ellanor") , recently started to not run well. She cranks right up and runs but when I increase speed, the rate of the engine running drastically drops until it finally dies. If I slow down and put it in neutral before I feel it about to die , - the rate of the engine running picks right back up and goes to how it should be. Then shortly after going forward again the cycle of it slowing down repeats itself. Also it vibrates excessively. I took off the deck and the problem persists. Please help ASAP I use this mower professionally and need her ticking right ASAP. Any feedback would be greatly appreciated. Thanks

We need to know what engine you have by model number please. The help you receive can vary depending on the engine.