Principle 1

Do not count Rabbinic Commandments in this list. E.g. lighting Chanukah candles or reciting the Hallel.

Indeed, this seems obvious, for the Talmud says that 613 mitzvot "were given to Moses at Sinai," and rabbinic mitzvot were not instituted until later dates. But in truth, we follow rabbinic rulings because of a biblical mandate: "You shall not divert from the word they tell you, either right or left" (Deuteronomy17:11); and as such, before performing a rabbinic mitzvah, we say a blessing in which we thank G‑d for "sanctifying us with His commandments and commanding us to..." Nevertheless, the individual rabbinic precepts are not counted as part of the 613 (and, are considered "rabbinic," a classification that has certain halachic implications).

Principle 2

Do not include laws which are derived from one of the Thirteen Principles of Torah Exegesis.

Every word and letter in the Torah is exact, and the Sages extrapolated many laws from an extra (or missing) word or letter, or a particular sequence which the Torah chooses to use (click here for more on this topic). Nevertheless, unless the Sages explicitly say that a particular law that they derived is categorized as biblical, it is not counted as part of the 613.

An example of this is the obligation to accord honor to parents-in-law, a precept derived from an extra word ("et") in a verse. Though the Torah alludes to the concept, it is not considered a biblical command.

Principle 3

Do not count mitzvot which are not binding on all generations. E.g. the laws regarding the disassembly of the Tabernacle, or the prohibition against waging war on Amon and Moab, which only applied to the Israelites in the desert.