If you have acess to Dremel or other rotary tool you can use a cutoff /abrasive wheel attachment to cut them off. They may have been inserted by a power tool that fires them in with a gunpowder charge. If this is the case prying them out will be difficult if not impossible. You could try a Sawzall but these type of fasteners are very hard and you will go through a lot of blades. Some type of cut off wheel or grinder is the way to go. You may forgo the expense of buying one by renting one. If you opt for the grinder you will be able to grind away a little of the concrete so the nail will be below grade. You can then patch the low spots to level the finished surface. Be aware that any type of cutting wheel you use will throw sparks and if you grind the concrete it will generate losts of dust so use appropriate safety precautions.
Use a prybar to lever up the treads about 1/8" and then use a Sawzall type reciprocating saw with a metal blade to cut the shank between the tread and the riser. Check to see if you can rent the reciprocting saw at a tool rental. The blades are readily available at any Hardware and Tool supply.
You won't be wanting to drive back into the same hole as the new spikes will have less grab in the wood anyway. Be sure to check the risers for rot.
Personally, I don't do spikes anymore, there are structural wood screws available that are a bit easier to install, can be removed and have better bite in the wood. Since you already have the spikes, Eastwing makes a nice 3-lb mason's hammer that would probably be better than trying to drive them with a 16oz framing hammer.
![enter image description here](https://i.stack.imgur.com/JBX0B.png)
Structural Wood Screws will be installable by drill motor, though you might want a 1/2" corded drill with a little torque behind it. Consult the manufacturer as most are self-drilling, needing no pilot hole.
They will be either Hex drive or Torx and the manufacturer usually provides the bits for quality control so the heads don't get bunged up during installation. The items and manufacturers below are chosen because they are recommended for timber framing and available in 10" lengths:
FastenMaster TimberLok (top) and HeadLok (bottom):
![enter image description here](https://i.stack.imgur.com/NrUjg.png)
![enter image description here](https://i.stack.imgur.com/kZmVr.png)
GRK Fasteners RSS (top) and RSS LTF (bottom)
![enter image description here](https://i.stack.imgur.com/DvOun.png)
![enter image description here](https://i.stack.imgur.com/0fkm3.png)
Simpson Strong-Tie SDWS (top) and SDWH (bottom)
![enter image description here](https://i.stack.imgur.com/rLidR.png)
![enter image description here](https://i.stack.imgur.com/Ap34S.png)
All these manufacturers will provide installation information, strength tables and recommendations on use. Lots of Acrobat files to read if you're so inclined.
Best Answer
Another method is to get pliers and a block of wood about the height of the extended nail ( protruding out the wood). Grab the nail out the side of the pliers and insert the block of wood between the joist and the head of the pliers. then use the leverage to pull the nail out, this is also great because it will not damage your wood.![enter image description here](https://i.stack.imgur.com/4GQPF.jpg)