Answer
The motion of the saw blade is SHM.
Work Step by Step
Let $t=0$ when the knob is at the bottom of the circle and let $\theta = 0$ be the angle at the bottom of the circle. Let $R$ be the radius of the circle that the knob follows. Let $x$ be horizontal component of the knob's position around the circle. Let $x = 0$ be the center of the circle.
We can find an expression for $x$ in terms of time $t$:
$\frac{x}{R} = sin~\theta$
$\frac{x}{R} = sin~(\omega~t)$
$x = R~sin~(\omega~t)$
Since the blade's back and forth motion is the same as the knob's horizontal component of motion, the blade's back and forth motion can be described with the equation $x = R~sin~(\omega~t)$, which is an equation for SHM.
Therefore, the motion of the saw blade is SHM.
