Your description leaves a lot to be desired, but it sure sounds like it's normal for this model.
Couple things.
First, yes, they are sluggish. And highly dependent on fluid temperature which affects the pressures inside the transmission. It's NOTHING like a car transmission. You shift gears. High and low and reverse those are the only "gears" it has. The speed increases and decreases based on the hydrostatic transmission which is controlled by a bunch of cables that also control the engine throttle.
Honestly if you don't know it's history, I'd suggest a full fluid and filters (there are 2) change. When replacing the transmission fluid, ONLY use Super UDT2 and nothing else. Regular UDT makes them even more temperature sensitive such that on cold mornings, when you mash the throttle, it's like dumping the clutch in overdrive....just kills the engine. Super UDT isn't as bad. But then as the temp comes up, say summer in West Texas, then the engine revs up a lot more and the transmission takes a while to really "catch up". This is a normal characteristic but can be minimized, in other words be made more consistent between temperature swings, by using Super UDT2 fluid-and nothing else (and yes I've tested several kinds of fluids).
Once the fluid and filters are known proper, you can look closer at the cable adjustments-they are very sensitive to proper adjustment per the work shop manual (WSM). VERY sensitive.
