when the music is is not too present, but still there, you can try a "dynamic" filter" (a least thats how it's named in premiere pro;
The settings are a bit complicated but basicly the trick is that you can boost the loud sounds while reducing to a minimum the lower ones (music).
So each time a word start the volume is boosed (or kept as the same level) and as soon as it stops, the volume is dropped to zero. That could prevent you the long task to do it manualy.
But this only really work when the music is not too loud, the spoken lines not too long, and if you add a music and new sound effects above to hide the trick.
To really remove unwanted music. You may try a filter you can find in Audacity called "noise removal".
Basicaly you select a segment of sound that is the kind of sound/frequencies you want to remove. Here the music.
So you first "get the noise profil"
Then you apply it to the part with the same kind of music with the voices on.
You have some settings to make the effect stonger or softer, but of course, the strongest you go, the more some frequencies of your voices will also be removed,
because they will surely share some of the frenquencies with the music. removing violin is particulary hard because it shares some same frenquencies with the human voice for example.
The only way to remove for sure a music from the voice is to have the exact same music without the voices. Soundtrack music from CD wont work. You'd need the exact same frenquencies, the exact same volume, everything. So, all in all, there is close to zero chance that this methode would work. But you can try:
Let's say you have an Elvis song in stereo, and the exact same song but only the instrumental version. Compression is same, volume is the same, it starts exactely at the same moment etc...
Well, if you open those two piece of music in Audacity and go: effect/invert on ONE of them... then there is a good chance you'll end with only the voice of Elvis. Because most of the time on records, the main voice is the only elements that is exactely the same on both left and right (along with the bass sometime...)
So this effect "invert" frequencies. And when two exact opposite frequencies are played at the same time: as strange as it is there is no sound to be heard.
I spent hours working on that last trick and came up with nothing good. But it's fun to try.