Snap to Grid is not a tempo based tool. It snaps to subdivisions of a measure. measure, Whole, Half, Quarter, etc.
If you're trying to remove sections of a track the Edit>Delete feature can be very handy as you can select a portion of a track and delete it, and remove the empty space (hole) when you delete... having the effect of bringing the segments before and after the deleted segment together.
This can sometimes have undesirable effects on the sound because it can leave you with very abrupt volume changes resulting in ugly sounding pops and clicks. To best blend in different segments of audio like this you can manually, or automatically, crossfade them. The first segment fades out as the next segment fades in. Done right the paste is seamless.
One way to manually do this would be to select an area exactly one eighth note after the beginning of the segment you want to remove, and one eighth note before the end of the segment. Use snap to grid set to eighth so that the deleted portion was exactly on the off- beat.
For example, let's say I want to keep measure 1 and 2, delete measure 3 and move the clip at measure 4 up to the beginning of measure 3. I would delete the section one eighth note after the beginning of measure 3 and one eighth note before the beginning of measure 4. After deleting that segment I would click and drag the clip starting at one eighth note before measure 4 so the beginning went to one eighth note before measure three. This would result in the audio that had started at measure 4 now starting at measure three and the audio one eighth note before and after the bar blending.
To make the clips automatically crossfade that options has to be set in Options>Global>Editing. You can also click and drag the top corner of a clip to fade it in or out.
This is just a general suggestion and the actual note increments you use can vary depending on the material and the tempo. Experiment and see what works best for you.
Really, it sounded a lot simpler in my head.
If your audio doesn't match the measures and beats at all it might be best to just delete the undesirable audio and remove the hole. Then if you have a problem with pops you can manually adjust the fade out/fade in of the clips you are joining.