Can I go to Yuntai Garden and Baiyun Mountain from Yue Xiu Park metro station in Guangzhou?

Yes, it is true.
You can get out of the Baiyun Park Station from Exit B and walk along the Jinyuan Road to find the Jin Xin Lu Kou Bus Station, where you can take the bus line 841 to Yun Tai Suo Dao (Yuntai Cable Car) Station. Then walk to the Yuntain Garden.

From Yuexiu Park Bus Station on North Jiefang Road, you can find bus line 24 to Yun Tai Hua Yuan Zong Zhan (Yuntain Garden General Station) and then walk the Yuntai Garden and the Baiyun Mountain.

Hope it helps ~