I am designing a 6-layers PCB and the requirement is that on the bottom layer there should be no holes,
Taken literally, this means you won't have any electrical connection from layer 6 to the other layers. Possibly you can solve this by filling your vias with epoxy, but you haven't made your requirements clear enough to know.
[I] could not find anything on mounting holes as blind.
This is because making a blind mounting hole wouldn't be useful for most applications. The point of a mounting hole is to pass a screw through it to mount the PCB to the enclosure of your system. You can't do this with a blind hole.
The mounting holes may also be used by your assembly (board-stuffing) shop to hold the board in their machinery. If you remove all through mounting holes, be sure to check with your assembly shop whether they need any other design features to compensate.
One solution might be to design your board with break-away tabs, and place any mounting holes required for the manufacturing process in the tabs. Then remove the tabs before using the board in the application where you have the no-through-hole requirement.
I have looked into the back-drill option
This doesn't make any sense. The point of back-drilling is to remove copper plating from parts of a via where it isn't wanted (usually for signal integrity reasons, when you have signals above 5 GHz or so). Since mounting holes aren't plated to begin with, there's no need to back-drill them.
Edit to Add
After seeing your comments, it seems like what you really want is unplated controlled-depth drills.
There's no particular reason this couldn't be done, but it will add cost.
The best way to find out the design rules you'll need to follow for this process is to call your PCB fab shop and ask.