The M3 thread is only 0.25mm deep, (Tapping size for M3 x 0.5 is 2.5mm) that is most unlikely to withstand the force needed to drag the Tailstock along the bed. So even with a new die, do use a Tailstock Die Holder, and lubrication. The only force imposed on the freshly cut thread will be that needed to slide the Die Holder along the Arbor, (which will be absolutely minimal).
Cutting a thread with a Die, in one pass, you are removing, relatively, a lot of metal. If you were cutting the thread with a single point tool, you would use several passes, with increasing depth of cut.
Using a handheld Die Holder, and resisting rotation by resting against the Bed, or the Toolpost, may tend to lever the die off the lathe axis, which will not improve the cut at all. The Arbor, mentioned above, allows the Die to pick up and follow the workpiece, but keeps it more closely aligned.
Howard