One thing I have learned is that in 6.1 you have to click or tap on the icon for the tag, and not the name, in order to multi-select. But that multi-select is enabled by default.
I took 3 screenshots. The first shows the tagspicker for Sites > Search > Tags in aem 6.1 author instance. See image open-sites-search-tags.png
If you click or tap on the name, it will select one and also "activate" it if it contains child tags - open the next column to show the child tags. See image activate-select-one-tag.png
If you ctrl-click the tag icon, you can add more to the selection. See image select-multiple-tags.png.
- JK
PS: the images are not appearing, I'll try in text comment.