Grumpy_Mike:
I hope you are not using it with 5V, The maximum voltage according to that sheet is 2.5V, you should not even be driving it with 3.3V. You should be driving it with 1.8V.
Note under the table of specifications where it says "Internal diode specifications only".
The module contains a constant current driver. It is intended to run from 3.3V. It almost certainly will tolerate 5V, but will heat up. The description makes no mention of duty cycle and a 25mW laser probably can run continuously with reasonable heatsinking or at least good air circulation around the casing.
In fact, at a 50% duty cycle, it almost certainly can run continuously, probably even on a 5V supply since the dissipation in the constant-current circuit will be reduced as well.
There are however, two other problems.
The most obvious is the specified current - 35 mA typical, 60 mA maximum. This is beyond the (safe) specification of the Arduino - whichever it is, so you need to use a transistor to drive it. Just about any general purpose NPN transistor will do. You could use a base resistor of about 1k from the Arduino port. Put two silicon diodes in series with the laser module and you have reduced 5V to 3.7V and allowing some loss in the transistor, that should be just about right.
The second is a bit more subtle. Not knowing what capacitors (or if any) are in the current driver, you do not know whether it is designed for pulsed operation at a given frequency. If its response it slowed by capacitors, it may either not turn on, or may overdrive the laser diode.
And you have not actually explained whether your test circuit has actually been working in the first place? What you have been doing may or may not be damaging, depending on the variation in the above factors. It would be useful to measure the current draw either continuously (from a 3.5V supply) or for comparison, when you are PWM-ing it, but a cheap multimeter will not indicate this on the 200mA range while the 10A range gives poor resolution (10 mA - at 3 digits).
Note that the actual current is set by the diode itself controlling the "ACC" circuit.
Oh yes! I just noted ...
This laser module is completely self contained and useful for sensor, biomedical and laser radar / laser radar jamming systems
This latter claim would imply that the module is OK to be (pulse) modulated. OTOH that may just be marketing! Also note that the casing is the positive terminal.