Nether portal mechanics: what happens if I destroy the overworld portal?

It doesn't affect the one in the Nether. Really when you reconstruct it again you teleport to the same place where you have an automatic portal. Same thing when you destroy the portal in the Nether and reconstruct it.

Nether portals do not have any long-term association with each other (there is a short-term destination cache). Destroying a portal will not affect any other portals.

When a player or entity passes through a nether portal minecraft will calculate the corresponding coordinates in the other dimension. It will then search around those coordinates for a nether portal. If it finds one the player or entity will be teleported there.

If a player passes through a nether portal and an appropriate destination portal cannot be found a location will be chosen near the calculated destination coordinates and a new portal will be generated. This is unlikely* to be in the same location as the portal you destroyed. I'm not sure if this also works for entities or not.

Many players prefer to build both nether portals by hand to get more control over their size and location.

* Unless the original portal was itself an automatically generated one and you thouroughly destroyed it.