It sounds like you may have a low production mud well. Despite it working well before on your old pump, it could simply mean that it was never properly developed to draw water at the rate your current pump does. If water is drawn slowly from the well, the well can recover and there is not the flow rate nor the differential pressure from the water level being drawn down to stir up the mud/sand.
Tell us more about the well, the depth, the casing size, the soil conditions, the recovery rate, the static level, etc. What GPM is the pump? What size is the pressure tank?
I have a very similar circumstance. When I had my well drilled before I built the house, the driller only pumped it at 5 GPM to satisfy the mortgage company requirement. After I built the house I put in a 10 GPM pump and it sucked up enough sand to not just plug the filter but it also jammed up the pump impeller. I shortened the drop pipe, but the mud rose up higher and jammed the impeller again. I had to get the driller back to flush out the well but by then the pump was damaged and no longer producing the GPM it should.
Fast forward 12 years... I finally had it with the old pump and decided I would try to develop the well to increase the recovery. I used the old pump to out pump the well recovery rate and washed out a lot of the mud. I managed to increase the recovery rate to what the old pump was capable of but did not want to subject my new pump to the abuse of the sand. I then dropped in my new pump and buttoned it up. The new pump is flow rate limited by the micronizer and so stirs up only small amounts of sand that the filter traps.
Back to your issue... You need to pull the pump and measure the depth of the well and the height of the water table. From that point you may have one or two choices. If there is enough water table, you may consider shortening up the drop pipe and then rate limiting the pump, but probably you will need to get someone in to flush out the well. Some drillers will use a large pump to push down thousands of gallons essentially pushing back some of the mud and flushing the rest out the top. Then you might consider putting down a small amount of stone to hold back the mud. Lastly, you need to develop the well by over-pumping until it runs clear.
