Fetching details from the dictionary...

to turn up; to roll up (e.g. sleeves)
to do over and over again; to do relentlessly; to do with reckless abandon; to do continuously
to stage a comeback (against) (in mahjong, horse racing, etc.); to come from behind
暑いので袖をまくって作業した。
It was hot, so I rolled up my sleeves and worked.
ズボンの裾をまくって川に入った。
I rolled up my pant legs and went into the river.
布団をまくったら猫が寝ていた。
When I turned up the blanket, a cat was sleeping there.