OK, so you know ten/ta/to (masculine/feminine/neuter for "this") and probably tamten/tamta/tamto (masculine/feminine/neuter for "that").
You are right, it is masculine Accusative, and this is when things get tricky. masculine Accusative is the only case when it is important whether the noun is animate or not. For feminine nouns, for neuter nouns, you don't care. But here, you do.
When the noun is inanimate, the Accusative form is identical to Nominative. "Ten stół jest zielony. Widzę ten stół." (This table is green. I see this table.)
When the noun is animate, however, the Accusative form is identical to Genitive. "Ten pies jest duży. Widzę tego psa. Nie widzę tego psa." (This dog is big. I see this dog. I do not see this dog.)
Firstly, it's too much of a simplification to talk about 'negative sentences'. The form of the word depends on the case. Different verbs, prepositions etc. need different cases. And indeed, those that took Accusative (the most popular case) take Genitive instead when negated.
"tego" is a masculine Accusative form for animate nouns (so it works for 'this dog' but not 'this table') and also generally a masculine Genitive form. So "We see this dog" is "Widzimy tego psa" and "We don't see this dog" is "Nie widzimy tego psa", this happens to be the same.
It is worth to take a look at the table here: https://en.wiktionary.org/wiki/ten#Declension_3