Hi Mr Turtle.
Captain Triggers made a good point in that it's often better to cut the main sprue to isolate the part in question then carefully cut the part from the seperated sprue piece using a "sharp" blade or fine saw, although some parts are moulded so fine and with so many sprue gates that no-matter how careful you are the part is impossible to remove without breaking it. The aerial mast for the Airfix Bf 109E springs to mind in this instance.
I've just completed a trio of Roden kits the Focker F.1, D.VI, & E.V / D.VIII, and many of the parts are so fine that it's impossible to seperate them from the main sprue tree without first cutting the sprue, even so I still managed to break two of the struts, luckily easily repaired or replaced with stretched sprue.
If using a scalpel just be careful cutting a thick-ish sprue gates as the blade can easily break if too much pressure is applied, and flying scalpel blades is something to be avoided. better to use an Ex-Acto type knife as these are much thicker and stronger. Side cutters should be available at any electonics parts store if your local model shop doesn't have any. Hope this helps.
Remember we do this for fun John the Pom