A vertical clutch device for a timepiece includes along a vertical axis a first wheel rotatably mounted about the vertical axis, a clutch disc, a spring, and a second wheel rotatably mounted about the vertical axis. The vertical clutch device is able to assume a clutched position where the second wheel is rotated by the first wheel under the action of the spring exerting a vertical force Fe to press the clutch disc against the first wheel and a disengaged position where the clutch disc is subjected against the action of the spring to a vertical force Fd separating it from the first wheel so that the second wheel is not rotated by the first wheel. The spring of the vertical clutch device is made of a shape memory alloy.