Ok, couple of ideas for you!
Lets do a very simple sandle test, can you mount him bare back? Does he do the same thing? You don´t need to ride him bar back, but will he stand to be mount, next to your block?
Is your mounting block high enough? If not you might be putting too much presure on the sandle as you mount.
Do you have to tighen the girth after mounting? If so there is a chance that the sandle is slipping as you mount. So check the girth prior to mounting and make sure the sandle is in a good position.
Have you got a friend / stable mate, that you could ask to mount your horse, see if your horse does the same thing, if not then there is a chance it is something you are doing.
Do you mount properly?
A lot of the time when a horse moves during mounting its to get their balance back.
SO if the problem is not with the sandle, lets just for a moment consider its something you might be doing wrong or that he has not been taught / miss understood.
Take horse to mounting block and stand with your horse untill he is calm and still.
Look at his stance are his front feet planted and is he secure in his balance? If his feet are not planted then his balance is not good then you can help him get his balance, by try to nudge him off of balance, gently of course. Were are tying to make this part of the mounting routine, each time he plants his legs quicker
Now stand next to him and put your foot in and out of the stirup untill he is not bothered by it at all.
Ok, so do not grab the sadle to mount.
Take the reins an place them along with your hand at the base of the mane (not the hair) you are holding firm but not pinching squeezing or pulling. This hand is to stabilise you its not a resting post, pivot point or anything else. The reins should help hold your horse still so make sure they are an appropriate lenght.
Put your Foot in the stirup check the position of your toes, they should not be pointing in towards the horse, but straight past his head (other wise you are going to toe him as you get over, and he is going to walk on) and swing your leg over without touching the horse, and over the other side, Settle gently into the saddle and find your other stirrup without looking, if possible. then remove your foot from stirup and adjust to the correct length if necessary
Now, STAND count to 15, 20, 25 whatever in your head until you horse is calm and then walk on (this will stop the come on mum lets go). Make sure you do not walk on untill your horse is calm THis it the great hurry up and wait, other wise he is always going to want to get on with the fun
If at any point he starts to drift or move about befor you mounted, Lift the reins, Don´t pull back, twist lift them up in the air wait for him to stop, take you foot out and start again. "to stop the drift, lift" We are trying to teach him that the more he "plays" or gets excited the longer it is going to take you to mount him properly. So the more "ready and well behaved" the quicker he will get what he wants (hacking)
Now there are a couple of things, as we get older we often don´t change our mounting, this is a mistake as sometimes we can´t lift our leg as high etc. So check that your mounting block is high enough.
I was also always taught to do regular mounting excercises to improve fitness,(horse and ours) on both sides this little drill together: down and up, down and up, down and up, stand halfway up, and when he stands still, reach over and rub him on the far shoulder to ask ?permission? to get on, and then get on!
One last thing that gets horses good about being dismounted is this: every time you dismount, do the same three-times drill (up-down, up-down, up-down). He?ll learn to stand still while you smoothly dismount.
Remember lots of praise, and smile it makes a difference