Start up fine runs smooth in park

Chevy siverado 3500 2003 - neutral but as soon as I shift into gear the car looses rpm Hi all im new here and really need your help. My chevy start up fine runs smooth in park and neutral but as soon as I shift into gear the car looses rpm sometimes even stalls. Also when im driving the car it will stall when I lift my foot of the gas to slow down it only does this when below 30kmh. The car had a full service including plugs, leads, oil, fuel, air filters, oil change, transmission oil, dif oil. This is just driving me crazy. I hope some one may be able to help diagnose this problem. Thanks to everyone in advance.