Hi, I am Helen Zhang, a professional Chinese teacher from eChineseonline.

The phrase “open the door” is translated into Mandarin “打开门(dǎ kāi mén).”
For examples:
Nǐ néng dǎ kāi mén ma?
你能打开门吗？
could you open the door?
Chinese phrase “open up” can be translated into “开发，开拓(kāifā, kāituò).”
For example:
Rúhé zài Zhōngguó kāituò xīn de shìchǎng?
如何在中国开拓新的市场？
How do you open a new market in China?