Yes, you can cut them.
First tip is to buy the size you need.
Second tip is if you need to cut that many, I wouldn't do it with a hand saw.
If you can leave the board un-cut, you'll save yourself time and effort and also allow you to spread the circuit out more (which is generally a good thing).
At the very least, build a couple before you cut down the boards just to make sure that it's practical to build them on the smaller board.
Oh and a third tip is that matrix board has to be the hardest way to make things in quantity.
I made 4 units of a small controller on matrix board. Whilst the first one (the prototype) was fine, and I got it working well, etc, reproducing it was a pain, and really time consuming.
I am relieved to find that nobody here recommended matrix board after knowing the quantity you needed to make.
I'd recommend you build a prototype, then test it. Once you're happy, document what connects to what and where each component goes (with orientation where required). Document from the copper side where connections are made and in what order. Use the leads of through hole components (like resistors) where possible to connect things.
Then build another one from the instructions and make sure it is identical to the first (and obviously test it)
Then set up a production line for maybe 10 units. Do step 1 on all of them, then step 2, then step 3, etc.
With matrix board construction, I'd probably recommend testing each unit, but after producing a batch, check at least one, and bag them up as a batch. If you find any of them have an error, you would be wise to suspect that the entire batch may have the same error.
Then, make up maybe 60 units in total so that if there are less than 10 failures during testing, you don't have to try to repair and diagnose them.
If you're planning to make 100, then make the first run of 50 first (that's 2 prototypes plus 60 units. If out of that 60 (the 2 prototypes should be kept as your reference units) you get 55 working units, those extra 5 mean that maybe you need only make 55 (if you're brave 50) to have a similar safety factor.
Oh and mark each unit with the batch number ant the number within the batch. Record which ones fail testing. If you end up selling, giving away, or having to maintain them, a record of where failures are (a particular batch perhaps?) will be very useful.
