It is a phrase that means "cut corners". It is used when describing situations in which you skip certain steps in order to do something as easy as possible. "手抜き" is a noun of "手を抜く".
"サボる" and "怠ける" are similar to "手を抜く". "サボる" and "怠ける" are used when you skip work/class. It is always used in a negative way.
On the other hand, 手を抜く" is used when you go to work/class but you slack off or you cut corners in a reasonable manner. It is used in both positive and negative ways.
Meg got home late at night and she is talking to her boyfriend.
- Meg: I'm so tired. Is it all right, if I made fuss-free recipes such as omurice tonight?
疲れたなぁ。今夜はオムライスとか、手抜き料理でもいい？ - Tom: Sure. I like it.
うん、いいよ。
She is taking care of her skin before going to bed.
- Tom: You should sleep early.
早く寝なよ。 - Meg: I know it, but I want to keep my skin healthy and glowing so I cannot cut corners with skincare.
うん。でも、肌を綺麗に保ちたいから、お肌の手入れだけは、手を抜けないよ。
Ken is worried about Leo because he has been working overtime everyday for more than two weeks.
- Ken: I'm leaving soon. I can give you a ride home.
そろそろ帰ろうかな。送っていくよ。 - Leo: No, thank you. I'm going to go through the documents one more time.
ありがとう、でもいいや。もう一度資料を確認したいんだ。 - Ken: You look tired. If you always try to be perfect, you might end up exhausted. I think it's important to know when to skimp on work.
疲れているみたいだぞ。いつも完璧でいようとすると疲れちゃうぞ。たまには手を抜かなきゃ。 - Leo: All right. I'll do it tomorrow.
そうだな。明日やるか。