Have a look at the package broom .
It has an easy way to pack the results in tables in the tibble format.
You can handle these tibbles (data.frames) in the standard way and e.g. select only certain columns.
See the example below.
I have no experience with creating Word documents from RMarkdown but it should work via RStudio with
File | New File | R Markdown | Word
I say 'should' because currently I can not knit the example file 
Edit: I wrongly saved the document with the R extension instead of Rmd. Corrected this and now it works. Use e.g. knitr::kable(df1) to see the table in your document.
mpg <- ggplot2::mpg
model<-lm(cty~displ,mpg)
summary(model)
#>
#> Call:
#> lm(formula = cty ~ displ, data = mpg)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -6.3109 -1.4695 -0.2566 1.1087 14.0064
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 25.9915 0.4821 53.91 <2e-16 ***
#> displ -2.6305 0.1302 -20.20 <2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 2.567 on 232 degrees of freedom
#> Multiple R-squared: 0.6376, Adjusted R-squared: 0.6361
#> F-statistic: 408.2 on 1 and 232 DF, p-value: < 2.2e-16
library(broom)
df1 <-tidy(model)
print(df1)
#> # A tibble: 2 x 5
#> term estimate std.error statistic p.value
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 (Intercept) 26.0 0.482 53.9 3.30e-133
#> 2 displ -2.63 0.130 -20.2 4.74e- 53
df2 <- glance(model)
print(df2)
#> # A tibble: 1 x 12
#> r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 0.638 0.636 2.57 408. 4.74e-53 1 -552. 1109. 1120.
#> # ... with 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>
Created on 2021-12-02 by the reprex package (v2.0.1)