We recently had the cable company install a phone line into our basement, as we use voice over cable as our telephone provider.

The "intelligent young man" who came to do this was to have just had the additional wire drape from the ceiling so that we could easily move the phone jack to the other side of the room, once we had some framework done. Well, he did NOT do this. He ran the additional wire along the electrical through the small holes drilled into the 2x4 that currently house the electrical wires as they drop down to each junction box.

My question is this, can I CUT the white/blue wires that come from the main phone line and then rewire them back together when they are relocated? If so, can this be done with wire nuts, or must we use a crimper.

Or, would it be best to cut off all of the lines currently fastened within the 3 line crimper and get a new crimper to wire it back together?

TIA!!

Would be best to unplug phone line at test point in outside box, then cut/disconnect rerun and reconnect. I woud not have splices not accessible, run phone/data from box to box or phone location(s), otherwise a buried splice may come back to haunt you.
I use "gel filled beanies" strip wires, twist for 1/2" and squeeze over connection, small wirenuts are commonly used.

This is probably the best way to handle the splice is the CAT 5E splice box:

Telephone & Network Connectors & Adaptors - HomeTech Solutions

But splices in walls are generally not a good thing. I also believe the standard distance to keep low-voltage from power lines is 6". Crossing perpendicular is oK, parallel is not inless 6" away. Home Depot and Lowe's, I think, sell Cat 5/CAT 5E by the foot, so you could put the splice in an accessible location.

This block requires a 110 punch down tool. Sometimes plastic ones are included.

As they say in the link, Don't splice, but run a new cable. You must maintain the twists when you splice.

Wirenuts are totally forbidden. Scotchlock connectors can be used, but the splice box is much better. The connectors use a parallel jaw plier to seat them correctly. Crimp connectors on solid wire never work.

EDIT: Perpendicular stuff added

I wouldn't have any junctions, just a phone plate, even if just for connecting.
Home run if possible, if an addition, may have to daisey chain.
The link that KISS provided has the beanies, they are about a third the was down the page, and are yellow, they say don't strip, I have repaired Many phone systems due to not stripping or not crimping hard enough.
Strip 1/2" twist tight, and use gel beanie. I wouldn't use non gell filled beanies.