A cutting device and a method for emergency cutting of a line in a well are disclosed. The cutting device includes a tapering guide including a narrow end portion and a wide end portion for feed-through of the line, the narrow end portion being placed, when in its position of use, at a lower position than that of the wide end portion; at least one sliding block arranged axially movable within the tapering guide; at least one cutting knife connected to the sliding block and directed inwards in the tapering guide; at least one releasable holding mechanism for standby holding of the at least one sliding block at the wide end portion of the guide, and for releasing the at least one sliding block in connection with emergency cutting of the line. Upon release, the at least one sliding block will move downward in the direction of the narrow end portion of the guide where it will force its at least one cutting knife with increasing force against the line until it is cut off.