The gemara says that the issur of being mevatel issur lichatchila only applies to an issur that is d'oraysa, not to an issur that is d'rabonon. Tosafos points out that the sugya of litra ketzios seems to assume that even for teruma on figs which is only d'rabonon there is an issur to be mevatel lichatchila? Tosafos answers that an issur that has an ikar in the Torah sucah as teruma, which is d'oraysa for דגן תירוש ויצהר, is like a d'oraysa in that one cannot be mevatel lichatchila. But muktzah which is a type of issur d'rabonon that has no source in the Torah, one can be mevatel lichatchila. The Rosh has an entirely different approach to answer this question. Just as the gemara does away with דבר שיש לו מתירין due to the fact that the issur has been burned and not intact, that is why when it is only an issur d'rabonon AND מיקלא קלי איסורא it is not a problem to be mevatel it lichatchila. It comes out that the Rosh would seem to hold that even if it is עיקרו מן התורה, so long as it is not intact, one can be mevatel it lichatchila, whereas Tosafos will hold that even when intact one can be mevatel lichatchila so long as it doesn't have an ikar in the Torah.
Within the approach of Tosafos, it is unclear what the rationale is behind the distinction of יש לו עיקר מן התורה or not. The simpler approach is that something which has a source in the Torah is a more chamur issur because the Rabbonon are just extending an issur that is recognized by the Torah, whereas an issur that is a creation of the chachamim is not as severe and therefore one is allowed to be mevatel it lichatchila. The problem with this approach is that the gemara on 3b that discusses an egg which is ספק נולד ביום טוב and is assur like a ודאי, the gemara says that according to Rabba it is an issur d'oraysa and therefore ספק דאורייתא לחומרא, but according to Rav Yosef and Rav Yitzchok who hold that it is only d'rabonon it should be permitted based on safeik d'rabonon l'kula. The gemara never mentions Rav Nachman who holds that the problem is muktzah. Why not? The simple answer is that the gemara rejected his opinion, but the Tosafos Yeshanim (printed on the margin) says that the reason the gemara doesn't address Rav Nachman is because muktzah is very chamur and כעין דאורייתא, so that muktzah is like hachana d'rabba where we say ספק דאורייתא לחומרא. Is it possible to fit Tosafos with the Tosafos Yeshanim? Tosafos considers muktzah to be something that has no ikar min hatorah, yet Tosafos Yeshanim considers it כעין דאורייתא. It seems clear that if Tosafos means that something which is ikar min hatorah is more chamur, and muktzah is more kal, it is very difficult to justify how we can say ספק לחומרא by the issur of muktzah.
Another approach to explain Tosafos distinction between עיקר מן התורה and אין עיקר מן התורה is that it has nothing to do with the severity of the issur. There can be issurim that are not ikar min hatorah yet they are more chamur (such as muktzah like the tosafos yeshanim says). The Shiltei Giborim says that something which has an ikar in the torah one cannot be mevatel because it is easily confused with a d'oraysa and one will come to be mevatel an issur d'oraysa lichatchila. But something which has no ikar in the Torah such as muktzah, even if it is technically very chamur, it is not quite a d'oraysa and not easily confused with a d'oraysa so one can be mevatel it lichatchila. According to this approach it is possible that Tosafos can fit with the tosafos yeshanim.