Sub-divide - yes, without much doubt. You would need to establish what parcel you're selling, new legal description etc.

Mortgage perspective - They will probably have you provide an appraisal based on your home and the land that is staying with it. This will be to see if the loan still stays within the LTV (loan to value) ratios of the loan program you're in.

Example...300k prop value now. Your loan was 240k (80% ltv). You pull off the piece of land and the property is now worth 250k and you owe 240k (96% ltv). This will send a lender into a tissy fit. This is drastic to prove a point. They may have you pay down the loan enough that it still meets the original loan guidelines.