The key search term for this residue is "pitch", like "removing pitch from blade".
A variety of products for cleaning pitch off of cutting tools are sold, many of which use a caustic chemical like that found in spray-on oven cleaner. You may have luck with oven cleaner itself, although those chemicals can remove other things in addition to pitch, like paint and other coatings, for example.
A technique I found amazing, and now use exclusively, is to soak in a hot-as-you-can-stand-it concentrated mixture of liquid laundry detergent and water. This video shows more of the details and produces results just like what I have seen myself: https://www.youtube.com/watch?v=nYnd6BGifoo
I use the same All detergent as shown in the video, just because that's what we have in the house, but I'm sure many others would work just as well.
Laundry detergent is a mild caustic, which perhaps explains its effectiveness, but I've never seen it do any damage to the blades I've cleaned this way.
Really hot tap water will work, boiling water is probably not advisable. As I recall, a 50-50 mixture of detergent to water is optimum. You don't need a huge amount if you use the right shape of container and you can clean multiple blades before refreshing the solution, perhaps warming it up a bit in a microwave between blades. I believe it works with cooler water, but the required soaking time is extended. The used solution can be safely poured down the drain, which of course is what happens when you use it to clean your clothes :)