14sb engine running when blade clutch is engaged

Normally I believe this mower to have a Kawasaki engine, and the main jet and 'pilot air hole' need to be cleaned. You are running a lean condition, and when the blade is engaged, the engine does not have enough fuel to continue the extra load. A small test for this is to engage the blade and the choke at the same time. If the engine has enough fuel to continue running and engage the blade, this confirms the lean fuel condition. Cleaning those jets will solve the issue.