The relation of transconductance is as follows (operation in saturation and ignoring channel length modulation)
gm = µn Cox (W/L)(Vgs-Vt)
as Vgs is increased it results in an electric field perpendicular to the channel (Ex) that accelerates the carriers towards the surface increasing scattering hence decreasing mobility and decreasing gm.
Also, the carrier mobility does suffer due to short channel lengths (2nd order effect). There is another component of electric field (Ey) parallel to the channel due to Vds. The mobility degradation effect due to Vds is more important than due to Vgs, because for high velocity values the velocity saturates.
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