My first question is about how long you've had this problem. Are either the tractor or the mower a newer purchase? Have you ever cut taller grasses with this mower when it didn't slow down?
My other question is, have you checked the hydraulic flow to your remotes? There's usually an adjustment that can limit flow, which means limiting your available power to the attachment.
Might also check (if you haven't already) your hydraulic level, as well as the hydraulic filters.
When I had a rotary cutter, it would bog down in taller grasses also. Reason being, they're specifically designed for thicker, more woody vegetation. They have thick blades. You "can" replace the thicker blades with thinner blades and your cutting in taller grasses will improve dramatically - just don't hit any stumps, logs or rocks!