If you cut out the dam now, the water will flow to the new pond location, and then a huge amount of soupy muck will ALSO flow to the new pond. IMO, that is the last thing you want for the new pond. You will immediately lose some of the depth you just paid to create.

Will surface runoff water to the new pond mostly flow in through the old pond? If so, then I think the old pond has some value as an upstream sediment trap. That will allow your new pond to have a much longer life.

Is the edge of the new pond going to be right up against the dam of the old pond? If so, then another option is to connect the two ponds. However, I would make the connection very shallow. For example, just cut down one foot deep into the old dam for the span of your proposed bridge.

Regardless of whether you connect the ponds, you should probably consider draining the old pond (away from the new pond) and performing a fish kill. Otherwise the undesirable fish in the old pond will make it over to the new pond and disrupt your fish stocking and management plans.

The experts on the forum (not me) have indicated many times that starting from scratch is usually much cheaper and much easier in the middle to long run.

Good luck on your pond projects!