The gemara says that the prohibition of bringing שאור ודבש, yeast and honey, on the mizbeiach only applies when it is being done לריח ניחוח - as an offering. But, if it is being done for the sake of fire wood, meaning not as an offering, there is no prohibition. The Rambam as explained by kesef mishna (issurei mizbeiach 5:3) holds that this only works if it is brought independently but not together with an actual korban. See Minchas Chinuch 117. However, there is a machlokes between the Rabbonon and R. Eliezer in the Mishna if one can burn limbs of a chatas לשם עצים, to be like firewood or whether this is only a heter to bring up yeast and honey on the mizbeiach. We pasken like the Rabbonon that the idea of bringing up for the sake of firewood only works for yeast and honey, but not for other korbanos that don't belong on the mizbeiach. Nevertheless, Tosafos 77b d.h. b'dam suggests that even the Rabbonon would admit that only on kodshim such as a chatas which should be eaten, cannot be brought on the mizbeiach even לשם עצים but the intent "for the sake of firewood" would work for chulin items to be put on the mizbeiach. It is for this reason that we would allow the blood of a korban that gets mixed with non-korban blood to be sprinkled and wouldn't constitute a violation of bringing chulin on the mizbeiach. The rationale seems to be that when something is brought with a korban or is actually a korban, one's intention can't remove that status. Therefore, it would be a violation of burning the meat of a chatas on the mizbeiach. Similary, when one burns the yeast and honey with a korban, it assumes status of a korban so that intent cannot consider it to be merely wood. But when one places chulin on the mizbeiach, since it doesn't belong there, the intent can consider it to be merely wood.
The Minchas Chinuch writes that the sacrificing of yeast and honey לשם עצים only works if it is explicit intent, but if it is done without any intent, it is a violation. It is not clear when one would burn chulin on the mizbeiach without any intent whether we would consider "stam" to be לשם עצים or whether we would require explicit intent לשם עצים to be patur. Tosafos seems to hold that this would also require specific intent.
On an Aggadah note - Sefer HaChinuch suggests that the issur to bring yeast on the mizbeiach is to remind us of zrizus and doing things quickly. The issur to bring honey on the mizebeiach is to teach that a person shouldn't spend their lives running after sweets, rather a person should focus on foods that are healthy for his body and he needs to sustain himself.
ספר החנוך (מצוה קי"ז) - ובענין הרחקת הדבש נאמר אל הילדים רכים כדי לייסרם, שהוא סיבה לדמיון שימעט האדם מלרדוף אחר המאכלים המתוקים לחכו כמנהגג הזוללים והסובאים ימשכו לעולם אחר כל מתוק, ולא יתן לבו כי אם אל המאכלים המועילים לגופו וצריכים למחייתו ושומרים בריאות אבריו. ולזה ראוי לכל בעל שכל לכוין במזונו ושתייתו, לא לכוונת הנאת מישוש הגרון