Is there a story to this mutation of meaning? Or is this shift of semantics connected to phonetic considerations only?
批 [pī] is originally 𢱧 (扌+𣬉), and 批 is a vulgar form since ancient times.
㧙 is another variant form, meaning wring, twist, strike at.
𢱧 thus means to strike with the hand, to slap, and also to kill.
《唐韻》匹迷切《集韻》《韻會》篇迷切，𠀤音鈚。《說文》手擊也。《左傳·莊十二年》宋萬遇仇牧于門，批而殺之。 又《廣韻》推也，轉也。 又示也。《唐書·李藩傳》遷給事中，制敕有不便者，黃紙後批之。 又《韻會》與(卑刂)通。削也。《杜甫·房兵曹馬詩》竹批雙耳峻。 又《集韻》騈迷切，音鼙。擊也。 又助也。 又頻脂切。與琵通。琵琶，馬上所鼓。或从手。《風俗通》批把，近世樂家所作，以手批把，因以爲名。 又《韻會》《正韻》𠀤普弭切，音庀。亦手擊也。 又《集韻》《韻會》𠀤蒲結切，音蹩。讀若敝入聲。義同。《史記·荆軻傳》奈何以見陵之怨，欲批其逆鱗哉。《註》批謂觸擊之。 又《孫臏傳》批亢擣虛。《註》批音白結反。相排批也。《莊子·養生主》批大郤，導大窾。 又《正韻》避列切，音別。義同。《韻會》通作㧙。《集韻》本作𢱧。
Here additional meanings are push, turn, peel, cut, help, and we also see that 琵琶 has been written 批把, a reminder that people always have had problems knowing characters.
http://www.zdic.net/z/1a/js/6279.htm informs of the modern meanings:
The principal meaning is still to hit with the hand, and to cut is also preserved as a basic connotation.
批 as a measure word or as a batch is rather recent, and might be the result of analogy or slang, for instance when bundling goods in the harbor.
Drunken Master points out that 批评 may be seen as an analogy to dissecting things in critique, but another possibility is that it just adds a slapping notion to the evaluation, since 批评 originally meant criticizing negative traits and shortcomings. Afterwards, it has yet again shifted to take on the connotation of critique in general, including praise and other positive meanings.