Ok so after going through OP's log its clear what happend, I will outline below.
So to begin you are in a Cutter with a few boosters and stock armour, this puts your shields around 700 MJ with an Armour value of 720, I also see from the log these shields are stock.
Timeline of events:
@ 16:24:58 - you are interdicted and submit (This is the correct thing to do unless you feel you can win the interdiction)
@ 16:25:00 - +2 sec, You drop from SC and are now in normal space, FSD cooldown begins now.
@ 16:25:09 - +9 sec, Combat begins, combat music is started. (you are already 9 sec into this! your cooldown is 1sec!)
@ 16:25:25 - +16 sec, Your shields are now down. (A FSD charge was not started! if you had you would be out by now... this is why you where killed)
@ 16:25:26 - +1 sec, Your hull is now at 80%!
@ 16:25:26 - +0 sec, Your hull is now at 60%!
@ 16:25:29 - +3 sec, The attacker was reloading in the time leading up to this even, Hull is now at 25%! (Hull integrity critical warning!)
@ 16:25:29 - +0 sec, Hull integrity is now 0% (you are dead!)
You did not even attempt to charge your FSD.
You where killed by an Imperial Clipper
Its clear the attacker was using Fragment cannons due to their reload time as shown in the log, it would seem they where using Double Shot Screening shells, this Clipper build allows for a DPS output of over 1200 with a basic build and ability to pilot, an advance player though this clearly wasn't can destroy your ship in less then 5 sec.
The CMDR that attacked you is well known to for their targeting of easy targets and unfortunate for bounty hunters... pulling the plug when things don't go their way.