a reciprocating saw will do it, but the wood must be dry. Wet or sappy wood will clog the blade.
Try it with the coarsest blade you can find, if the saw suits you, try to get a TCT blade which will be more expensive, but stay sharp much longer.
I have a feeling you don't want a chainsaw.
If you are cutting branches off standing trees, a manual bow-saw will be much less likely to cut your arm off, and, if sharp, is a pleasure to use.
If you get a mains-electric saw, it is essential that you either use an RCD-protected socket, or an RCD adaptor (sold in gardening and DIY shops) at the house end of the extension cable to protect you from shock after you cut through the cable. Test the RCD before each use, as they don't last forever.
You will need some kind of sawhorse to hold the timber securely while you cut it, or it might roll or fall over while the saw is running.
Gloves, safety specs etc.