Alexander Sorry, I think Spinebot's answer was confusing, so I added a strikeout.
On the Spine editor, multiple animation combinations can be previewed using the Preview view. However, there is no functionality yet to save the combination. This is one of the features we hope to add in future versions, and an issue for this enhancement can be found here: EsotericSoftware/spine-editor371
With the Spine runtime, you can play multiple animations simultaneously and export them in still or video format. We especially recommend using Unity with the Timeline extension, which is very useful and allows you to combine multiple animations and export them in a variety of formats without writing a single line of code. Please see the tutorial video that explains how to use it:
https://www.bilibili.com/video/BV1Ze411N75S/