Hackzall vs oscillating multi-tool

If you're talking about tools like this, then you can use them vertically.

The manual for the tool I linked to doesn't have any mention of the words horizontal, vertical, level, flat or upright, so if they don't warn you not to, you can assume it's OK to do it.

One thing to note is that to sand a vertical surface, you're going to have to hold the tool more tightly than you would if you were working on a horizontal surface. This will cause more vibration to be transferred to your hand and wrists, which will tire them out more quickly. If you're doing a large area, this can cause repetitive strain injury; when I sanded some window frames a while back, it took a couple of days afterwards for my wrist to feel OK again.

Like you, I find it more effective as a cutter through harder surfaces if you move the blade across the surface you wish to cut. I also apply light pressure to the tool while "sawing" with it.

Although in your case, it probably was simply that the wood was very hard.