It sounds as if a slide is probably jamming slightly, as you say. There are several things that can cause this, however. One is lack of lubrication, another is too tight a fit, and a third is misalignment or cocking of one part when it tries to slide. Whether lubrication is appropriate depends on whether there is dirt exposure, but even if it is out in the dirt, you can clean it and apply some dry graphite powder. Too tight a fit, when the parts have been in use previously, usually means one of the parts is damaged, or packed with dirt. Cocking of one part usually means incorrect assembly.
If nothing is jamming, you may not have attached some part of the cutter clutch linkage correctly.
The reason I do not like sticking cutter clutches, is it seems possible that under some circumstances, you might end up with the clutch engaging after a delay, when you had forgotten the lever was in the engaged position. This could result in somebody being injured.
