Speed and mass can effect the relative time of 'another' object or person. Nothing will affect the way time passes for you, or in your own frame of reference.
When an object is in a powerful gravitational field or moving very quickly relative to you, you would observe that time - including the rate of radioactive decay - in this other frame would be slower. An observer in that frame would perceive that your time was slowed. But if you were in that frame, time would pass for you as it always has, and radioactive decay would also proceed as it always has.
The mechanism of this slowdown from mass is to be found in General Relativity, in the way mass causes a distortion of space-time that may be undifferentiable from acceleration, but not because of an acceleration. In a similar way, the way time distorts in relative frames of motion is also an effect of space-time distortion of observers.
It is important to realize that in no case is there any absolute or objective change in the passage of time. If two observers, one travelling at .7 times the speed of light relative to the earth, and the other travelling at .9 times the speed of light relative to the earth were to observe the passage of time on the earth, they would each observe that the passage of time here was slowed, but each would observe that it was slowed by a different rate.