Short answer
Theoretically yes. The BIP-39 wordlist has only 2,048 words — losing 1 word takes at most 2,048 tries; losing 2 words requires about 4.2 million tries, still doable on a regular laptop in a few hours. Three prerequisites: you must know exactly which slot is missing, the other words must be in perfect order, and you must run the recovery on a fully air-gapped device with open-source tools. If you only know one or two words are missing but not their positions, the search space explodes.
Why this works
BIP-39 mnemonics carry a built-in checksum — the last 4 bits in 12-word mnemonics, last 8 bits in 24-word mnemonics, computed as a truncated SHA-256 hash of the entropy. This means a randomly inserted word has only a 1-in-16 chance of "accidentally" passing the checksum. The mechanism works the other way for brute-force recovery: the program tries 2,048 candidates per slot, the checksum filters out almost all of them, and the surviving candidates are few.
The tools
The fastest path for a single missing word is iancoleman/bip39 (the open-source mnemonic split branch) or btcrecover (a dedicated password-recovery project). Both available on GitHub. Download to an air-gapped computer, run with the known words in their known positions, get a candidate list within minutes — usually a few dozen to a few hundred. Import each into a watch-only wallet and check which one matches your expected address. For two missing words, the same tools work but expect to wait several hours.
Critical safety rule
Never run any mnemonic-recovery tool on an internet-connected device. The Ledger Donjon team has documented multiple cases where mnemonic-recovery websites quietly logged every attempted phrase to a remote server, including the eventually successful one. Use a freshly installed Linux laptop with no network drivers, or a Tails USB stick.
Further reading: Private keys and seed phrases, BIP-39.