First of all, what bike do you have??
Next, have you adjusted the clutch lifter, as opposed to the clutch cable? There's actually three adjustments on the clutch: the lifter, the lower cable adjuster, and the upper cable adjuster. Adjust the lifter first, then the lower adjuster, then the upper adjuster.
As a diagnostic, adjust the lifter slightly too tight, so that the clutch doesn't engage fully. Now when you pull in the lever you'll be sure there's no drag on the clutch that's loading the transmission down. If you can now upshift from first to neutral, then clutch drag is the issue.
mystic_1