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.
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):
GRK Fasteners RSS (top) and RSS LTF (bottom)
Simpson Strong-Tie SDWS (top) and SDWH (bottom)
All these manufacturers will provide installation information, strength tables and recommendations on use. Lots of Acrobat files to read if you're so inclined.