Most of the vital activities of Israel as they were camped in the wilderness took place at the tabernacle in the midst of the camp. On the other hand, there are in the Scriptures about thirty references to things that had to take place "without the camp." The event described in our text is the first of these. The people had not yet come into covenant relationship with God, but were just about to encounter Him at Mount Sinai.
Once they had committed themselves to the covenant of law, the only events required to take place outside the camp had to do with keeping intact the holiness of the camp itself. For example, lepers were made to remain "without the camp" (Leviticus 13:46), because of both the infectious nature of the disease and also the fact that leprosy is used in the Bible as a type of sin. Those who were convicted of blasphemy against God were stoned "without the camp" (Leviticus 24:14), and this was also done in the case of those who ignored God's Sabbath rest day (Numbers 15:35). All the bodies of animals slain as sin-offerings had to be "burned without the camp" (Hebrews 13:11).
All of these were also types of the Lord Jesus Christ, the ultimate sin-offering for the sin of the whole world. "Wherefore Jesus also, that he might sanctify the people with his own blood, suffered without the gate" (Hebrews 13:12). In Jesus' time on earth, there was no camp as such, so He was taken outside the city walls for execution.
As a result of the willingness of the Lord Jesus to die for us, we are exhorted to die to self and live unto Him. "Let us go forth therefore unto him without the camp, bearing his reproach. For here have we no continuing city, but we seek one to come" (Hebrews 13:13-14). HMM http://www.icr.org/article/6119/