This is how I see it. Sporting director sits at the very top of the football pyramid and is answerable to the CEO who tackles business as well. He's basically the CEO for the sports section. Below him there's the manager (tactics, team morale, coaching), head scout (scouting), head of academy (academy) and technical director (who monitors the transition of academy players to first team) etc.
The advantage of that setup is that it protects the manager on many counts Take Antony for example. ETH keeps playing Antony because he is 'his signing' and if he tanks then that reflects badly on him. Also note that if an influential player gets too old and he doesn't deserve to keep earning his huge salary then its easier to get rid of him without the manager suffering the repercussions of player power. That's because if morale tanks then the maximum players can achieve is to sack the manager whom (99%) will take the players side. That what happened at Juventus when they decided that it was time for Del Piero to go.
The trouble with that setup is that the departments are so distinct that they do not work with one another. That what happened at Inter for example during Silvestre's time. The manager would ask for a striker only for him to end up with 2 LBs simply because Branca (DOF/Sporting director) believed that the squad needed a LB more then he needed a striker. United had struggled with this as well. For example its evident that VDB (Ole) and Fred (Mou) weren't wanted by the manager.
Thus you need someone whose role is to coordinate all stakeholders (manager, scouts, head of negotiating, academy, data analysts) and make sure that everyone is on the same page and aiming for the same goal. His also on the constant lookup on bargains (ie he would want to be the first to know that player X wants to leave), building relationships with clubs and agents and to know if player Y who seem a genius on the pitch has any negative character traits (ex he tend to play FIFA till early morning). Let's not forget that the average player today cost 60m + will probably earn 150k a week for let's say 5 years. That's another 40m. So the last thing the club wants is to spend 100m on the wrong type of player.
Now the sporting director has too much on his plate to go through every transfers and involve himself at every step in every deal (ins and outs). The scouts, the data analysts and the transfer negotiator can tackle an aspect of a transfer. What brings all together transfer wise is the head of recruitment or something of that kind (clubs might have different titles for that type of job)