It's a supporting wall. Appropriately-sized steel or flitchplate headers over the door openings will substitute for the removed blocks or concrete.

When you cut the block you will need pressure-treated lumber on each side of the opening so it can be wrapped with finished materials i.e trimmed opening, casing, etc if you plan on finishing the space and you can have a basic header suitable for the opening width to carry the above load-bearing right on it.

How wide is the doorway opening you plan on making? It can be done in many ways and it's very easy to do... An experienced contractor will know what needs to be done and it's easy to do, the hardest part is to cut the block and clean up the opening so it can be finished.

That being said, you will have to have a drawing, apply for a permit, and have the work inspected.

Here are a few examples to give you an idea of what is involved. Using lumber for everything is the easiest and fastest way.

This is option 2 using a concrete lintel but you still need the lumber to trim everything out

Good luck

Thank you so much for these diagrams!! They are so helpful. Our wall is actually poured concrete as opposed to blocks, but I imagine this applies to both scenarios.

If you are cutting a large hole for a window or door in a poured concrete foundation, typically that is on an exterior wall. There is room because the grade is dug out for that window or door, the sawcuts are made, the slab leaned out, chained, lifted by the skidsteer and taken to the street.

Inside your house, it will be very difficult to bring any slabs up the stairs. And, there is lots of water/smoke/debris dust that occurs with sawcutting or breaking. Sawcuts are priced by the length, so more cuts for smaller pieces is lots more money. Or, concrete breaking, in the vertical plane, is very time consuming and laborous. So be prepared for a very intrusive and pricey endeavor.

If this completely changes the use of the basement for the better and the logistics doesn't scare you, contact a local structural engineer.

Here's a good video (terrible music) showing the process.

The good thing is that this sort of job doesn't usually attract "handymen", so you can choose a pro. As suggested above, include the task of removing the cut piece(s) in the price.

I've seen walls cut without watered blades. Dust clouds everywhere!