Agrupe por múltiples columnas en un solo procedimiento almacenado MySql

Sí, es posible usar un SQL dinámico . Podemos crear una cadena de consulta y luego prepararla y ejecutarla. Esto nos permitirá especificar el nombre de la columna dinámica, lo que no es posible directamente.

También deberá usar un parámetro más para especificar qué columna usar en Group By

DELIMITER $$

CREATE DEFINER=`root`@`localhost` 
  PROCEDURE `GetChartApprovedData`(in siteValue varchar(45),
                                   in skillValue varchar(100), 
                                   in shiftValue varchar(100), 
                                   in tmValue varchar(45), 
                                   in grpmValue varchar(45), 
                                   in dateValue date, 
                                   in dateValue1 date, 
                                   in groupByColumn varchar(64)) 
-- add extra in parameter, groupByColumn, to specify which column to group upon 

BEGIN

SET query_str = CONCAT('SELECT 
                          count(agentlogin) AS totalApproved, 
                          shift AS Shift, 
                          skill AS Skill, 
                          tm AS TM, 
                          grpM AS GrpM
                        FROM approved
                        WHERE (sitevalue IS NULL
                               OR site = sitevalue)
                          AND (skillvalue IS NULL
                               OR skill = skillvalue)
                          AND (shiftvalue IS NULL
                               OR shift = shiftvalue)
                          AND (tmValue IS NULL
                               OR tm = tmValue)
                          AND (grpmValue IS NULL
                               OR grpM = grpmValue)
                          AND (dateValue IS NULL
                               OR date BETWEEN dateValue AND dateValue1)
                        GROUP BY ', 
                        groupByColumn); -- concatenate the group by column param

-- prepare the query
PREPARE stmt FROM query_str;

-- execute the query
EXECUTE stmt;

-- Clear up
DEALLOCATE PREPARE stmt;

END $$

DELIMITER ;