On a METAR, what does DSPTD mean?
This is a METAR with the addition of U.S. Observations, and according to the details of the abbreviations used there is no such value as DSPTD. 

I suspect you are right, that it should have been DSIPTG - which does indeed mean "dissipating". The full decode of the Remarks section of your example METAR is as follows


A02 - automated station with precipitation descriminator.
PK WND 35037/0325 - Peak wind 350 degrees at 37 knots between 03 and 25mins
RAB04 - Rain began at 04mins (You can infer the hour from the main report)
PLB25 - Ice pellets began at 25mins (Again, inferring the hour from the report) 
TS DSPTD - Thunderstorms which dissipated
P0000 - Trace amount of  hourly precipitation


I should add that I'm by no means an expert at decoding this part of a METAR, I made judicious use of this page.