Jose, except for starting from a stand-still, you don’t use the clutch at all. All upshifts and downshifts are performed without using the clutch.
My guess is that your clutch cable might be stuck or misadjusted, preventing the clutch from engaging fully. Also, an upshift reduces torque so it is strange that the engine does not lower rpm’s on upshifts but the rpm’s are increasing for downshifts (I assume). If the clutch was going to slip it should do it when the torque increases.
Which leads to my next thought, which is that your upshifts are not upshifts at all. Sometimes the shifter mechanism can become misadjusted or run into interference with a seat strut. You pull back on the lever and it seems to move, but in fact there isn’t enough travel to move the tranny into a higher gear. This used to happen to me on an older shifter (usually mid race, of course) when the engine mount would slip back a bit and the shift rod started hitting a seat strut and couldn’t move far enough anymore. This only happens on upshifts because that moves the lever on the engine back toward the rear of the kart; there was plenty of room to pull if forward and downshift.