If you intentionally cut bread slices with a meat knife, can you then eat that slice of bread with dairy products?
In the Shulchan Aruch it was generally assumed that knives had some amount of residue on them, so the answer would be a simple "no."
I know rabbis who you'd consider "modern Orthodox" who feel this still applies today -- if you look carefully at the serrations -- so the answer would still be "no." I know other rabbis who you'd consider "ultra-Orthodox" who have said today's knives are cleaner (thank you, modern detergent technology, and stainless steel) so there may be more room for leniency.
So take a very careful look at the knife, then ask your local rabbi.