Runner cutting layer of tissue (3)
I believe the answer is:
ski
'runner' is the definition.
(something which 'runs', ie moves quickly on snow)
'cutting layer of tissue' is the wordplay.
'cutting' means to remove the last letter.
'layer of tissue' becomes 'skin' (layer of tissue on the body).
'skin' with its last letter removed is 'SKI'.
(Other definitions for ski that I've seen before include "Sport on piste" , "Sliding runner" , "go uphill? Probably not!" , "Walk on snow" , "Glide or race across snow with feet attachments" .)