Thread Cut Test
To find out if the moving and fixed knife are able to cut thread, you can perform the test shown in the animation on the right.  Remove the needle plate, hold the moving knife open as shown, and loop 2 strands of thread over the inside crook of the knife.  Allow the knife to spring closed under the fixed knife to check how effective cutting action is.

Stuck Pin Collar
If the moving knife appears to be correctly in-time but still does not fully extend the knife, check to see that the engagement pin rises cleanly out of its housing.  As shown in the animation below, the collar that the pin normally sits in when retracted can sometimes come loose and rise up together with the pin.  This collar normally holds the pin steady and in place, which in turn allows the pin to firmly deflect as it is moved by the groove of the cam.  But when the collar slides up, out of its housing, it allows the pin to wobble as it engages with the knife cam groove, preventing it from effectively actuating the knife.