Swap, delete and repeat
Retina, 44 20 bytes

Crossed out 44 is still regular 44 :(

+`'(\w).(.*).\B
$1$2


Assumes input in following format (in unary - counting character: '):
{number of repeats}{string}
For example: '''''''ABCDEFGHIJKLMNOP
There is no space between number of repeats and the string.

Thanks @MartinBüttner for shaving off 24 bytes!

Try it online!